Bending and Twisting Lattice Tilt in Strained CoreâShell Nanowires

Subscriber access provided by CORNELL UNIVERSITY LIBRARY

Communication

Bending and twisted lattice tilt in strained core-shell nanowires revealed by nanofocused X-ray diffraction Jesper Wallentin, Daniel Jacobsson, Markus Osterhoff, Magnus T Borgström, and Tim Salditt Nano Lett., Just Accepted Manuscript • Publication Date (Web): 14 Jun 2017 Downloaded from http://pubs.acs.org on June 15, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Bending and twisted lattice tilt in strained core-shell nanowires revealed by nanofocused X-ray diffraction Jesper Wallentin1,2 *, Daniel Jacobsson3,4, Markus Osterhoff1, Magnus T. Borgström3, Tim Salditt1 1

Institute for X-Ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

2

Synchrotron Radiation Research and NanoLund, Lund University, 222 62 Lund, Sweden

3

Solid State Physics and NanoLund, Lund University, Box 118, 221 00 Lund, Sweden

4

Centre for Analysis and Synthesis, Lund University, Box 124, 221 00 Lund, Sweden.

KEYWORDS Nanowires, strain, core-shell, X-ray diffraction, transmission electron microscopy

ACS Paragon Plus Environment

1

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 29

ABSTRACT We have investigated strained GaAs-GaInP core-shell nanowires using transmission electron microscopy and nanofocused scanning X-ray diffraction. Nominally identical growth conditions for each sample were achieved by using nanoimprint lithography to create wafer-scale arrays of Au seed particles. However, we observe large individual differences, with neighboring nanowires showing either straight, bent or twisted morphology. Using scanning X-ray diffraction, we reconstructed and quantified the bending and twisting of the nanowires in three dimensions. In one nanowire, we find that the shell lattice is tilted with respect to the core, with an angle that increases from 2° at the base to 5° at the top. Furthermore, the azimuthal orientation of the tilt changes by 30° along the nanowire axis. Our results demonstrate how strained coreshell nanowire growth can lead to a rich interplay of composition, lattice mismatch, bending and lattice tilt, with additional degrees of complexity compared with thin films.


2

Page 3 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Epitaxial core-shell nanowires are created by first growing an axial core nanowire and then changing the conditions to promote shell growth1. Core-shell nanowires can be used to create novel nanostructures2, and have shown promise in applications such as light-emitting devices3, catalysts4, energy storage5, solar cells6, 7 and electronic devices8. Strain created provides critical performance enhancement in modern electronics,9 and has been used to tune the electronic band gap in nanowires10-12. The interplay between lattice mismatch, strain and defect formation is well understood in lattice mismatched thin film heterostructures, where there is a critical thickness above which defects form. Theoretical modeling has predicted that strained core-shell nanowires could have a higher critical shell thickness than the corresponding thin film systems,13, 14 while experimental studies have shown that strained core-shell growth can lead to the formation of quantum dots15, uneven shell growth16, and defects17, 18. For several reasons, core-shell nanowires are more complex than thin films. First, nanowires can bend much more easily than wafers due to their thin diameter19-23. Second, nanowires have several simultaneous growth facets, not just one, and bending affects opposing facets differently. In contrast, theoretical models typically assume a cylindrical symmetry.13, 14 Also, the strain can vary substantially from the middle of the facets to the corners, which in turn can affect the composition of the grown layers15, 24. Third, the crystal structure can vary depending on growth conditions, which affects the growth rate of the subsequent shell17, 25. The complexity of strained core-shell nanowires requires advanced tools for characterization, and the methods employed include photoluminescence10,

11, 26, 27

, Raman spectroscopy26,

27

,

cathodoluminescence28, 29 and electron microscopy17, 30, 31. X-ray diffraction has excellent strain sensitivity,32 but the real-space resolution has historically been poor. Recent developments in


3

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 29

high-brilliance synchrotron sources and X-ray optics have however allowed investigations of individual nanostructures19, 33-39. In this letter, we show electron microscopy and nano-XRD investigations of single strained GaAs-GaInP core-shell nanowires (Fig. 1A). The nanowires exhibit considerable bending and twisting, much larger than the wafer bowing occuring in thin film growth, which we reconstruct and quantify in three dimensions. In addition, we observe that the lattice in the shell of one nanowire is tilted with respect to the core, with a direction that twists along the nanowire axis. GaxIn1-xP is an important compound for light-emitting and light-absorbing devices, since the bandgap can be tuned from near infrared to the middle of the visible spectrum. At a composition of about x = 0.51, it is lattice matched to GaAs. The sample discussed here was part of a series of growth runs with a large range of molar fractions of the Ga precursor in the shell, which were all investigated using SEM and lab-source XRD. Before growth, GaAs (111)B substrates were covered with Si3N4. Using nanoimprint lithography, 100 nm diameter openings (pitch 1 µm) were made in the Si3N4, and covered with Au seed particles40,

41

. This method yields nominally identical growth conditions for the

nanowires, where the Si3N4 layer prevents substrate growth. Then, core GaAs nanowires were grown using a horizontal flow Aixtron 200/4 low pressure MOCVD using arsine (AsH3) and trimethyl gallium (TMGa) as precursor gases at molar fractions of 5.4x10-5 and 2.2x10-5, respectively, with substrate rotation. The axial growth temperature was set to 710 ºC, which results in pure zinc blende crystal structure. The nanowires grow in the (111)B direction with the (111) planes orthogonal to the long axis. To suppress axial growth during GaInP shell growth, the nanowire cores were taken out from the reactor and the Au seed particles were removed using a cyanide based Au etchant (TFAC


4

Page 5 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

from Transene). Shell growth was carried out in the same MOCVD as the core, using phosphine (PH3), trimethyl indium (TMIn) and TMGa as precursors at molar fractions of 1.5x10-2, 8.9x10-6 and 4.3x10-6, respectively. The shell growth temperature was set to 600 ºC. The (111) reflection of the as-grown core-shell nanowire sample was investigated using a Bruker D8 lab source XRD. The illuminated area of the sample was a few mm2, which means that signal from more than 106 nanowires was recorded. For the measurement, the detector angle (2θ) was scanned in steps of 0.005° between 26.437° and 28.572°, while the sample-angle (ω) was kept at ω=2θ/2. Structural investigation of single nanowires was done with transmission electron microscopy (TEM; JEOL 3000F and Hitachi HF3300S at 300kV) and elemental mapping with X-ray energy dispersive spectroscopy (XEDS; Oxford Instruments X-Max) in scanning TEM (STEM) mode. Samples for TEM analysis were prepared by transferring broken off nanowires onto lacey carbon-coated Cu grids. For high resolution TEM imaging, the nanowires were tilted to have the 〈101〉 zone axis orthogonal to the image plane. A 〈211〉 direction is hence parallel to the image plane, which also allows for elemental mapping of both the concave and convex side of bent nanowires. To prepare for the nano-XRD measurements, nanowires were deposited on a 1 µm thick Si3N4 membrane substrate (Silson). The X-ray beam at the ID-11 beamline at the ESRF synchrotron, Grenoble, France (photon energy 18 keV, flux 1.4×109 ph/s), was focused vertically using compound refractive lenses to a size of 100 nm vertically and 6 µm horizontally. We used a combination of optical microscopy and scanning X-ray microscopy to deterministically align a specific nanowire in the X-ray focus42. Note that the TEM analysis was not done of the same individual nanowires as the nano-XRD, since the 1 µm thick Si3N4 membrane is opaque for


5

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 29

electrons. Scanning nano-XRD was performed by acquiring rocking curves, that is, small scans in rotation around the (111) Bragg angle, at points with 100 nm distance along the nanowire axis (0.5 s integration time). The scattering of the (111) reflection from each rocking curve, as recorded by a Maxipix pixel detector, was mapped into reciprocal space, and the position of the Bragg peak, q(z) = (qx, qy, qz), was evaluated with peak fitting.19 The orthogonal reciprocal space coordinate system, shown in Fig. 3a, has the main component qz nominally parallel with the nanowire axis (|q|≈ qz). The (111) lattice plane distance is d111 = 2π/|q|. The orthogonal components qx and qy are oriented orthogonal and parallel with the Si3N4 substrate plane, respectively, but are not necessarily related to a specific crystal direction. First, the as-grown nanowires were investigated using SEM. The core-only GaAs nanowires have hexagonal cross-sections with 110- type facets, parallel with the 110- type cleaved edges of the substrate. The nanowires are around 3.8 µm long and the cross sections are asymmetric, with non-identical size of the facets. SEM of the finished core-shell nanowires also show 110- type facets, and with a large individual variation in morphology despite the nominally identical growth conditions (Fig. 1B-C). There is also a substantial length variation of nearby nanowires, from 3.2 to 4 µm. Some nanowires (type ‘I’ in Fig. 1C) do not exhibit any discernible bending, others are bent (‘II’), while yet others are twisted (‘III’). The nanowires that did bend, show a tendency to bend in the direction of the corners, i.e. in the six available 211type directions. We do not observe any preferred direction between these six directions. The bending is stronger near the edge of the sample. In the other samples in the growth series (not shown), we observe that the bending is more pronounced at lower TMGa molar fractions. Four nanowires were investigated with TEM and EDS. The crystal structure is pure zinc blende, without wurtzite segments, stacking faults or twins. HRTEM shows dense fringes


6

Page 7 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

indicating significant strain (Fig. 2A), which also prevents atomic resolution imaging. The composition was investigated with EDS line scans along and across the nanowire axis (Fig. 2BC). As Ga is present in both core and shell, the Ga signal was not possible to use in calculations of the shell composition. Instead, we used the ratio between the In and P signals. Since every other atom in the shell is P, an In/P ratio of 1 corresponds to a GaxIn1-x P composition of x = 0 (pure InP). The measured shell composition at the base of the individual nanowires is between x = 0.3 and x = 0.4. In three out of four nanowires, we observe that the In composition increases in the growth direction, by about 5 to 10 percentage points. The fourth nanowire showed a constant composition. Axial variations in composition of GaxIn1-x P and other ternary nanowires has been previously observed

43-46

, and is usually explained by differences in gas and surface diffusion

lengths between Ga, In, and their precursors. EDS line scans across the nanowires indicate differences between bent and straight nanowires, although it was difficult to quantify (not shown). In the straight nanowires, the shell was about 20-25 nm thick, surrounding a 120 nmdiameter core. In one bent nanowire the shell was thicker on the outside (convex) side, about 30 nm, compared with about 10 nm on the concave inside. We did not observe any compositional differences between the concave and convex side, but we note that this is challenging to determine in such a thin shell. The entire series of samples of different TMGa molar fraction were investigated with labsource XRD, and the result from the sample discussed in this letter is shown in Fig. 1D. Two peaks can be identified: The GaAs peak from the nanowire cores, and a second peak due to GaxIn1-x P growth. We fit the measured data with a double-Gaussian model, and found that the peaks are centered at 1.9167 and 1.9210 1/Å, with FWHM peak widths of 0.0059 and 0.0033 1/Å, respectively. The average lattice mismatch between core and shell is 0.22 %, and the core is


7

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 29

tensile strained about 0.21 % compared with unstrained GaAs. In the sample of nanowires grown with slightly higher TMGa molar fraction (not shown), there is a single peak and no observable bending in SEM, indicating lattice matched growth. Since this is in agreement with the TEM analysis, we conclude that the sample investigated here has a too low Ga fraction for lattice matching. Lab source XRD has a large spot size, which gives a valuable statistical average of an ensemble of nanostructures. However, individual nanostructures can differ substantially from the average33, and nanostructures can have internal variation as observed by TEM in our nanowires. Such variations only generate peak broadening in lab-source XRD.47 We therefore investigated two nanowires (A and B) with nanofocused scanning XRD using a synchrotron source (Fig. 3A). The first nanowire (A), displayed in Fig. 3, exhibits a single diffraction peak. We plotted the intensity of the Bragg peak vs. the vertical coordinate, z, showing a significant variation along the nanowire axis (Fig. 3B). A perfectly straight core-shell nanowire with constant composition would show a single vertical line in such a plot, or possibly two vertical lines for a sufficiently large lattice mismatch. The Bragg angle can vary due to variations in lattice plane distance, but also due to real-space tilting of the lattice. By mapping the diffraction data to reciprocal space, the variations of the (111) lattice plane distance, d111(z)= 2π/|q(z)|, could be separated from variations in tilt, corresponding to variations in the orthogonal components qx and qy. Fig. 3C shows that d111 is approximately constant in the lower half of the nanowire, d111 = 0.3276 nm, and increases towards the top to d111 = 0.3282 nm. Relaxed GaAs has d111 = 0.3264 nm, demonstrating that, as expected, the core was in tensile stress (varying from about 0.4 to 0.6 %) from the shell. The d111 variation corresponds, according to Vegard’s law, to a change in Ga composition in the GaxIn1-x P shell from x = 46.5% at the base to 44% near the top. The absolute


8

Page 9 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

values of x are larger, i.e. closer to lattice matched, than those from the TEM-EDS measurements. Since nano-XRD measures the lattice constant of the shell, which is compressively strained by the core, the nano-XRD measurements overestimate the Ga concentration. Another possible explanation for the discrepancy is that beam damage in the TEM causes P desorption, leading to an inflated In/P ratio. The components qx and qy should be constant for a straight nanowire, which was the case for the lower half of nanowire A. However, qx and qy varied significantly in the same region as the gradient in |q|, i.e. the upper half, due to bending of the nanowire19. Since the (111) planes are orthogonal to the nanowire axis, q(z) is locally parallel to the tangent of the single-crystal nanowire, and the contour of the nanowire can be reconstructed by stepwise integration19. The position rN of the nanowire axis at point N can be approximated as: = + /||, where dz = 100 nm is the step size. The base (z = 0) was used as reference, where x = y = 0, and the orthogonal positions were integrated towards the tip. The shape of the nanowire is visualized in 3D, as shown in Fig. 3E-F, using d111 for the color mapping. In the figure we have shown the position and orientation of the nanowire relative to the growth substrate, assuming that the base of the nanowire was orthogonal to the growth substrate at z = 0, rather than relative to the Si3N4 membrane which was used for the measurements. The 3D reconstruction shows that the nanowire is strongly bent in the upper half, while the lower half is straight. It can be observed in the top view of the reconstruction, along the z-axis (Fig. 3F), that the nanowire is twisted rather than bent in a simple arch. Bending has previously been quantified with nano-XRD in homogeneous InP nanowire devices, where it was induced by stress during processing.19 However, here the bending is much larger, making it noticeable also


9

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 29

in the SEM of the deposited nanowire (Fig. 3G). Twisted nanowires can also be observed in the SEM of the as-grown nanowires (type III in Fig. 1C). The second nanowire, B, shows two distinct Bragg peaks along most of its length (Fig. 4A). The split in Bragg angle is over one degree at the base of the nanowire, which is far more than the lattice mismatch could create. The reciprocal space mapping shows that one peak has an almost constant d111, while it increases for the second peak from the middle to the top (Fig. 4B). We therefore interpret the second peak as coming from the shell. While the shell lattice constant at the base is almost the same as for nanowire A, d111 = 0.3277 nm, at the top the shell shows d111 = 0.3288 nm, which is significantly more than the top of nanowire A. The relative increase in lattice constant along the nanowire axis is 0.33%, compared with 0.18% in nanowire A. Note that we could not observe a Bragg peak from the core above z = 3.1 µm. The reason for this is unclear, but we speculate that the orientation of the core changed sufficiently to put it out of the scanned angular region. In the lower region of the nanowire, |qcore| ≈ |qshell|, but we still observe two distinct peaks on the detector. The reason is that the orientation of qcore is different from qshell. Above z = 1.8 µm we find that |qshell| < |qcore| , i.e. dshell > dcore. We observe a discontinuity of the direction of qshell around z = 2.7 µm, which divides the shell into two regions. At this point the shell changes orientation abruptly, while |qshell| decreases continuously. We also calculated the difference between the orthogonal components, (qshell – qcore), to quantify how the orientation of the shell differs from the core. Then, this difference was converted into angles in a spherical coordinate system, with one polar angle (relative to the q3 axis), θ, and one azimuthal angle, φ, (relative to the q1 axis) (Fig. 4C). To visualize the complex crystal structure, we first reconstructed the shape of the nanowire using the qcore data, similarly to nanowire A. Then, we added circles to the figure to represent the orientation of the shell, with the


10

Page 11 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

color showing the lattice plane distance of the shell (Fig. 4D). The tilt of the planes in the plot were magnified for better visibility. The 3D reconstruction shows that nanowire B bends, again enough to be observable in SEM (not shown), but unlike nanowire A it exhibits no twisting. The magnitude of the bending is similar to nanowire A, and it is oriented approximately midway between the x and y axes. At the same time, the orientation of the shell lattice is approximately constant for z < 2.7 µm, which can also be seen in the constant qx and qy components of the shell (Fig. 4B). The polar θ angle represents a lattice tilt between shell and core, which increases from θ = 2° at the base to θ = 5° at the top. Since the nanowire bending is oriented approximately midway between x and y, while the shell lattice was tilted in the negative y direction, the relative azimuthal orientation of the tilt changes from about φ = -87º near the base, to φ = -57º at the top. Thus, the shell lattice twists around the core. The results show both bending, which has previously been observed16, 20-23, and lattice tilt in the strained core-shell nanowires. Kavanagh et al.

22

and Rigutti et al.

20

studied core-shell

nanowires with very strong compressive stress from the shell, and observed thicker shell on the inside of the bent nanowires. Conversely, there is a small tensile stress from the shell in our nanowires, and indeed we observe a slightly thicker shell on the outside of the bent nanowires. The bending reduces the lattice size on the concave side and increases the lattice size on the convex side. The magnitude of the bending can be quantified using the θ(z) curve, since the curvature at small angles is given by κ = dθ/dz and the radius of curvature is ρ=1/κ42. In the bent upper half of nanowire A, we find that the radius of curvature is approximately constant, ρ ≈ 45 µm. With this result, we can use Euler–Bernoulli beam theory to make a rough estimate of how the bending affects the crystal lattice. For a homogenous beam of diameter d = 160 nm, bending


11

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 29

leads to compression on the concave side and tension on the convex side which is ε = ±d/2ρ ≈ ±0.18 % (total difference 0.36 %). In the nanowires, the shell thickness is actually asymmetric, but this estimate shows that the bending can give lattice changes of similar magnitude as the lattice mismatch. Furthermore, a rough estimate of the expected curvature, given the lattice mismatch and the geometry, can be given by Stoney’s equation for a bilayer film48: = 6ℎ /ℎ , where m is the ratio of biaxial elastic constants (m ≈ 1). Here, we assume a constant lattice mismatch, ε = 0.5 %, that the substrate thickness is the core thickness, hs = 120 nm, and that the film thickness, hf = 20 nm, is simply the thickness difference between the two sides of the asymmetric shell observed in TEM. With these assumptions, we find ρ = 1/κ ≈ 24 µm, which is of the same order of magnitude as the observed value. A full theoretical model of the expected bending, from the geometry and the lattice mismatch, would require a three-dimensional model. To understand how the bending appears, one must remember that it starts already during growth. Consider a spontaneous difference in shell thickness, possibly initiated by a birth and spread growth mode, which leads to a small bending. The substrate lattice for the subsequent layer is then less mismatched on the convex side, which enhances the growth rate, and vice versa for the concave side. As the asymmetry of the shell thicknesses increases, the bending also increases and the process becomes self-amplifying. In our case, it is also possible that the composition of the shell could grow asymmetrically, but we could not discern such a gradient from our measurements. The reason for the initial asymmetry is unclear. One speculation is shadowing, which is unlikely since we used a sample holder with rotation and we did not observe any overall preferential directions in the bending. We note that the core nanowires had asymmetric sizes of the facets, which may affect surface diffusion or nucleation barriers for the


12

Page 13 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

subsequent shell growth. The twisting that can be clearly observed in SEM and nano-XRD, is a change of orientation of the bending along the nanowire axis. However, the cause for the twisting is not clear. Note that the radius of curvature in our nanowires is many orders of magnitude smaller than the wafer bowing observed in thin film heterostructures. Thus, bending in core-shell nanowires is a much stronger and more complex process than wafer bowing. Lattice tilts, here observed in nanowire B, are previously known from growth of strained heteroepitaxy of thin films49-51, but those tilts were at most on the order of 0.1-0.4°. Ayers and Ghandhi showed that lattice tilt only appears if the substrate is miscut a few degrees,51 which in our nanowires would effectively correspond to a tapered core. Although we could not measure any tapering in the core nanowires, it is unlikely that the facets are perfectly vertical. If we assume a slight normal tapering, i.e. that the nanowire is thicker at the base than at the top, the miscut is oriented in positive z. On the convex side of the nanowire, where the growth is faster, the lattice tilt is then oriented away from the surface normal, which is qualitatively consistent with observations from thin film growth.51 Ayers and Ghandhi also discussed how the formation of defects can lead to tilted growth.51 We are unable to directly observe defects, but one indication of such a defect is the sharp change of lattice direction at z = 2.7 µm, paired with a large split in lattice constant between core and shell. Note that nanowire B shows a stronger gradient in the shell composition, suggesting a larger mismatch between shell and core that would promote defect formation. In conclusion, our results demonstrate how scanning nano-XRD can reveal rich and novel epitaxial relationships within nanocrystals. While large area XRD only shows an average of many nanocrystals, our measurements exhibit striking differences between individual nanowires. Furthermore, the high spatial resolution reveals large variations within single nanowires, which


13

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 29

would be blurred by a lower-resolution method. Recently sub- 5 nm nanofocusing of hard X-rays has been demonstrated52, offering a clear path to improved spatial resolution of nano-XRD. This could allow a distinct signal separation of the core and shell in nanowires such as ours. Alternatively, coherent diffractive methods such as Bragg CDI53 or Bragg ptychography54 could be used to achieve sub-beam size spatial resolution. We show that growth of strained core-shell nanowires is far more complicated than strained layer growth, which is important for the design of such systems. Since the core is a very flexible and multifaceted substrate, the shell epitaxy has new degrees of complexity. The stress does not only lead to lattice strain and possibly defects, as often assumed, but can also result in strong nanowire bending and lattice tilts.


14

Page 15 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

FIGURES

Figure 1: A) Drawing of the GaAs-GaInP core-shell nanowire structure (not to scale). The nanowires are about 3.5 µm long with a core diameter of 120 nm and a 10-30 nm thick shell, as discussed in the main text. B) SEM of as-grown core-shell nanowires, tilt 30°. C) Top-view SEM, along the (111) axis, of the same sample as in B). The labels I, II, III refer to straight, bent and twisted nanowires, respectively. D) Lab-source XRD of the as-grown core-shell nanowires. The plot shows measured data as well as a fit from a double-Gaussian peak model. The peaks are centered at 1.9167 and 1.9210 1/Å with FWHM peak widths of 0.0059 and 0.0033 1/Å, respectively. The dashed line indicates the calculated peak position for unstrained GaAs.


15

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 29

Figure 2: Electron microscopy. A) HRTEM of the base region of a core-shell nanowire, B) Scanning electron microscopy image of another nanowire, imaged using a secondary electron detector in the same TEM as in panel A). C) The plot shows the ratio of the In and P concentrations in the nanowire in B), vs. the axial position along the nanowire, as measuredd using an EDS line scan. The red curve is a linear fit, with slope -0.029 µm-1 (standard error 0.011 µm-1).

Fig 1

Fui


16

Page 17 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3: Scanning X-ray nanodiffraction of nanowire A. A) Drawing of the experiment, with the reciprocal space coordinate system. The vertical real-space coordinate, z, is parallel with the nanowire axis. The size of the X-ray focus was 0.1 x 6 µm. B) Total counts in the Bragg peak on the detector, as a function of Bragg angle and the real-space coordinate along the nanowire axis, z (logarithmic color scale). C) The length of the scattering vector |q(z)|, and the lattice plane distance d111. D) The orthogonal components of scattering vector, qx and qy, vs. z. E) 3D reconstruction of the nanowire. The point at z = 0 µm was used as reference where x = y = 0. Note that the x and y scales are in nm and the z scale is in µm. The reconstructed nanowire has been rotated such that it is perpendicular to the substrate (grey) at z = 0 µm, which is the orientation of the as-grown nanowires. F) Projections of the 3D reconstruction in F), along the principal axes. G) SEM of nanowire as deposited on Si3N4 membrane. The straight yellow line is a guide to the eye.


17

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

Figure 4: Scanning X-ray nanodiffraction of nanowire B. A) Total counts of the Bragg peak on the detector, as a function of Bragg angle and z (logarithmic color scale). B) The length and the orthogonal components of the scattering vector, q, vs. z, for the core and the shell peaks. C) The angles between the scattering vectors of the shell lattice, qshell, and the core lattice, qcore, vs. z. The spherical coordinate system is also shown, with the azimuthal angle φ and the polar angle θ. D) 3D model of the nanowire, projected along the principal axes. For clarity, only half of the measured directions of the shell has been shown, and the tilt of the shell has been magnified. The color scale, which is the same for core and shell but different from Fig. 3, indicates the (111) lattice plane distance d111. The point at z = 0 µm was used as reference where x = y = 0. Note that the x and y scales are in nm and the z scale is in µm. The reconstructed nanowire has been rotated such that it is vertical at z = 0 µm, which is the orientation of the as-grown nanowires.


18

Page 19 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

AUTHOR INFORMATION Corresponding Author * Email: [email protected] Author Contributions D.J. and M.B grew the nanowires, and D.J. performed the electron microscopy. J.W., M.O. and T.S. performed the nano-XRD measurements and the data analysis thereof. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors thank Sarah Hoffmann for assistance with measurements. The authors acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and would like to thank Jon Wright for assistance in using beamline ID-11. Financial support by the Röntgen-Ångström Cluster, the K. A. Wallenberg Foundation, SFB 755 “Nanoscale Photonic Imaging” of the Deutsche Forschungsgemeinschaft, NanoLund, Marie Sklodowska Curie Actions, Cofund, Project INCA 600398, and the Swedish Research Council grant number 201500331 is gratefully acknowledged.


19

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

REFERENCES (1) Lauhon, L. J.; Gudiksen, M. S.; Wang, C. L.; Lieber, C. M. Epitaxial core-shell and coremultishell nanowire heterostructures. Nature 2002, 420, 6911, 57-61. (2) Hauge, H. I. T.; Verheijen, M. A.; Conesa-Boj, S.; Etzelstorfer, T.; Watzinger, M.; Kriegner, D.; Zardo, I.; Fasolato, C.; Capitani, F.; Postorino, P.; Kölling, S.; Li, A.; Assali, S.; Stangl, J.; Bakkers, E. P. A. M. Hexagonal Silicon Realized. Nano Lett. 2015, 15, 9, 5855-5860. (3) Tatebayashi, J.; Lin, A.; Wong, P. S.; Hick, R. F.; Huffaker, D. L. Visible light emission from self-catalyzed GaInP/GaP core-shell double heterostructure nanowires on silicon. J. Appl. Phys. 2010, 108, 3, 034315-5. (4) Koenigsmann, C.; Santulli, A. C.; Gong, K.; Vukmirovic, M. B.; Zhou, W.-p.; Sutter, E.; Wong, S. S.; Adzic, R. R. Enhanced Electrocatalytic Performance of Processed, Ultrathin, Supported Pd–Pt Core–Shell Nanowire Catalysts for the Oxygen Reduction Reaction. J. Am. Chem. Soc. 2011, 133, 25, 9783-9795. (5) Cui, L.-F.; Yang, Y.; Hsu, C.-M.; Cui, Y. Carbon−Silicon Core−Shell Nanowires as High Capacity Electrode for Lithium Ion Batteries. Nano Lett. 2009, 9, 9, 3370-3374. (6) Tang, J.; Huo, Z.; Brittman, S.; Gao, H.; Yang, P. Solution-processed core-shell nanowires for efficient photovoltaic cells. Nat. Nanotech. 2011, 6, 9, 568-72. (7) Goto, H.; Nosaki, K.; Tomioka, K.; Hara, S.; Hiruma, K.; Motohisa, J.; Fukui, T. Growth of Core–Shell InP Nanowires for Photovoltaic Application by Selective-Area Metal Organic Vapor Phase Epitaxy. Appl. Phys. Express 2009, 2 (2009) 035004. (8) Jiang, X. C.; Xiong, Q. H.; Nam, S.; Qian, F.; Li, Y.; Lieber, C. M. InAs/InP radial nanowire heterostructures as high electron mobility devices. Nano Lett. 2007, 7, 10, 3214-3218. (9) Lee, M. L.; Fitzgerald, E. A.; Bulsara, M. T.; Currie, M. T.; Lochtefeld, A. Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors. J. Appl. Phys. 2005, 97, 1, 011101. (10) Bouwes Bavinck, M.; Zieliński, M.; Witek, B. J.; Zehender, T.; Bakkers, E. P. A. M.; Zwiller, V. Controlling a Nanowire Quantum Dot Band Gap Using a Straining Dielectric Envelope. Nano Lett. 2012, 12, 12, 6206-6211. (11) Wojnar, P.; Zielinski, M.; Janik, E.; Zaleszczyk, W.; Wojciechowski, T.; Wojnar, R.; Szymura, M.; Kłopotowski, Ł.; Baczewski, L. T.; Pietruchik, A.; Wiater, M.; Kret, S.; Karczewski, G.; Wojtowicz, T.; Kossut, J. Strain-induced energy gap variation in ZnTe/ZnMgTe core/shell nanowires. Appl. Phys. Lett. 2014, 104, 16, 163111. (12) Hetzl, M.; Kraut, M.; Winnerl, J.; Francaviglia, L.; Döblinger, M.; Matich, S.; Fontcuberta i Morral, A.; Stutzmann, M. Strain-Induced Band Gap Engineering in Selectively Grown GaN– (Al,Ga)N Core–Shell Nanowire Heterostructures. Nano Lett. 2016, 16, 11, 7098-7106. (13) Trammell, T. E.; Zhang, X.; Li, Y.; Chen, L.-Q.; Dickey, E. C. Equilibrium strain-energy analysis of coherently strained core–shell nanowires. J. Cryst. Growth 2008, 310, 12, 3084-3092. (14) Haapamaki, C. M.; Baugh, J.; LaPierre, R. R. Critical shell thickness for InAsAlxIn1−xAs(P) core-shell nanowires. J. Appl. Phys. 2012, 112, 12, 124305. (15) Heiss, M.; Fontana, Y.; Gustafsson, A.; Wüst, G.; Magen, C.; O’Regan, D. D.; Luo, J. W.; Ketterer, B.; Conesa-Boj, S.; Kuhlmann, A. V.; Houel, J.; Russo-Averchi, E.; Morante, J. R.; Cantoni, M.; Marzari, N.; Arbiol, J.; Zunger, A.; Warburton, R. J.; Fontcuberta i Morral, A. Selfassembled quantum dots in a nanowire system for quantum photonics. Nat. Mat. 2013, 12 439– 444.


20

Page 21 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(16) Lewis, R. B.; Nicolai, L.; Küpers, H.; Ramsteiner, M.; Trampert, A.; Geelhaar, L. Anomalous Strain Relaxation in Core–Shell Nanowire Heterostructures via Simultaneous Coherent and Incoherent Growth. Nano Lett. 2017, 17, 1, 136-142. (17) Conesa-Boj, S.; Boioli, F.; Russo-Averchi, E.; Dunand, S.; Heiss, M.; Rüffer, D.; Wyrsch, N.; Ballif, C.; Miglio, L.; Morral, A. F. i. Plastic and Elastic Strain Fields in GaAs/Si Core–Shell Nanowires. Nano Lett. 2014, 14, 4, 1859-1864. (18) Dayeh, S. A.; Tang, W.; Boioli, F.; Kavanagh, K. L.; Zheng, H.; Wang, J.; Mack, N. H.; Swadener, G.; Huang, J. Y.; Miglio, L.; Tu, K.-N.; Picraux, S. T. Direct Measurement of Coherency Limits for Strain Relaxation in Heteroepitaxial Core/Shell Nanowires. Nano Lett. 2012. (19) Wallentin, J.; Osterhoff, M.; Salditt, T. In operando X-ray diffraction reveals electrically induced strain and bending in single nanowire device. Adv. Mater. 2016, 28, 9, 1788-1792. (20) Rigutti, L.; Jacopin, G.; Largeau, L.; Galopin, E.; De Luna Bugallo, A.; Julien, F. H.; Harmand, J. C.; Glas, F.; Tchernycheva, M. Correlation of optical and structural properties of GaN/AlN core-shell nanowires. Phys. Rev. B 2011, 83, 15, 155320. (21) Cai, X. M.; Leung, Y. H.; Cheung, K. Y.; Tam, K. H.; Djurišić, A. B.; Xie, M. H.; Chen, H. Y.; Gwo, S. Straight and helical InGaN core–shell nanowires with a high In core content. Nanotechnology 2006, 17, 9, 2330. (22) Kavanagh, K. L.; Saveliev, I.; Blumin, M.; Swadener, G.; Ruda, H. E. Faster radial strain relaxation in InAs–GaAs core–shell heterowires. J. Appl. Phys. 2012, 111, 4, 044301. (23) Hilse, M.; Takagaki, Y.; Ramsteiner, M.; Herfort, J.; Breuer, S.; Geelhaar, L.; Riechert, H. Strain in GaAs–MnAs core–shell nanowires grown by molecular beam epitaxy. J. Cryst. Growth 2011, 323, 1, 307-310. (24) Sköld, N.; Wagner, J. B.; Karlsson, G.; Hernan, T.; Seifert, W.; Pistol, M. E.; Samuelson, L. Phase segregation in AlInP shells on GaAs nanowires. Nano Lett 2006, 6, 12, 2743-7. (25) Wallentin, J.; Messing, M. E.; Trygg, E.; Samuelson, L.; Deppert, K.; Borgström, M. T. Growth of doped InAsyP1-y nanowires with InP shells. J. Cryst. Growth 2011, 331, 1, 8-14. (26) Montazeri, M.; Fickenscher, M.; Smith, L. M.; Jackson, H. E.; Yarrison-Rice, J.; Kang, J. H.; Gao, Q.; Tan, H. H.; Jagadish, C.; Guo, Y.; Zou, J.; Pistol, M.-E.; Pryor, C. E. Direct Measure of Strain and Electronic Structure in GaAs/GaP Core-Shell Nanowires. Nano Lett. 2010. (27) Signorello, G.; Lörtscher, E.; Khomyakov, P. A.; Karg, S.; Dheeraj, D. L.; Gotsmann, B.; Weman, H.; Riel, H. Inducing a direct-to-pseudodirect bandgap transition in wurtzite GaAs nanowires with uniaxial stress. Nat. Comm. 2014, 5, 3655. (28) Wei, B.; Zheng, K.; Ji, Y.; Zhang, Y.; Zhang, Z.; Han, X. Size-Dependent Bandgap Modulation of ZnO Nanowires by Tensile Strain. Nano Lett. 2012, 12, 9, 4595-4599. (29) Haizhou, X.; Nan, P.; Ming, L.; Yukun, W.; Xiaoping, W.; Hou, J. G. Probing the strain effect on near band edge emission of a curved ZnO nanowire via spatially resolved cathodoluminescence. Nanotechnology 2010, 21, 21, 215701. (30) Larsson, M. W.; Wagner, J. B.; Wallin, M.; Håkansson, P.; Fröberg, L. E.; Samuelson, L.; Wallenberg, L. R. Strain mapping in free-standing heterostructured wurtzite InAs/InP nanowires. Nanotechnology 2007, 18, 1, 015504. (31) Jones, E. J.; Ermez, S.; Gradečak, S. Mapping of Strain Fields in GaAs/GaAsP Core–Shell Nanowires with Nanometer Resolution. Nano Lett. 2015, 15, 12, 7873-7879. (32) Chahine, G. A.; Richard, M.-I.; Homs-Regojo, R. A.; Tran-Caliste, T. N.; Carbone, D.; Jacques, V. L. R.; Grifone, R.; Boesecke, P.; Katzer, J.; Costina, I.; Djazouli, H.; Schroeder, T.;


21

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 29

Schulli, T. U. Imaging of strain and lattice orientation by quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping. J. Appl. Crystallogr. 2014, 47, 2, 762-769. (33) Mocuta, C.; Stangl, J.; Mundboth, K.; Metzger, T. H.; Bauer, G.; Vartanyants, I. A.; Schmidbauer, M.; Boeck, T. Beyond the ensemble average: X-ray microdiffraction analysis of single SiGe islands. Phys. Rev. B 2008, 77, 24, 245425. (34) Williams, G. J.; Pfeifer, M. A.; Vartanyants, I. A.; Robinson, I. K. Three-Dimensional Imaging of Microstructure in Au Nanocrystals. Phys. Rev. Lett. 2003, 90, 17, 175501. (35) Chamard, V.; Stangl, J.; Labat, S.; Mandl, B.; Lechner, R. T.; Metzger, T. H. Evidence of stacking-fault distribution along an InAs nanowire using micro-focused coherent X-ray diffraction. J. Appl. Crystallogr. 2008, 41, 2, 272-280. (36) Newton, M. C.; Leake, S. J.; Harder, R.; Robinson, I. K. Three-dimensional imaging of strain in a single ZnO nanorod. Nat. Mat. 2010, 9, 2, 120-124. (37) Hanke, M.; Dubslaff, M.; Schmidbauer, M.; Boeck, T.; Schöder, S.; Burghammer, M.; Riekel, C.; Patommel, J.; Schroer, C. G. Scanning x-ray diffraction with 200nm spatial resolution. Appl. Phys. Lett. 2008, 92, 19, 193109. (38) Hrauda, N.; Zhang, J.; Wintersberger, E.; Etzelstorfer, T.; Mandl, B.; Stangl, J.; Carbone, D.; Holý, V.; Jovanović, V.; Biasotto, C.; Nanver, L. K.; Moers, J. r.; Grützmacher, D.; Bauer, G. n. X-ray Nanodiffraction on a Single SiGe Quantum Dot inside a Functioning Field-Effect Transistor. Nano Lett. 2011, 11, 7, 2875-2880. (39) Haag, S. T.; Richard, M.-I.; Welzel, U.; Favre-Nicolin, V.; Balmes, O.; Richter, G.; Mittemeijer, E. J.; Thomas, O. Concentration and Strain Fields inside a Ag/Au Core–Shell Nanowire Studied by Coherent X-ray Diffraction. Nano Lett. 2013, 13, 5, 1883–1889. (40) Berg, A.; Yazdi, S.; Nowzari, A.; Storm, K.; Jain, V.; Vainorius, N.; Samuelson, L.; Wagner, J. B.; Borgström, M. T. Radial Nanowire Light-Emitting Diodes in the (AlxGa1– x)yIn1–yP Material System. Nano Lett. 2016, 16, 1, 656-662. (41) Otnes, G.; Heurlin, M.; Graczyk, M.; Wallentin, J.; Jacobsson, D.; Berg, A.; Maximov, I.; Borgström, M. T. Strategies to obtain pattern fidelity in nanowire growth from large-area surfaces patterned using nanoimprint lithography. Nano Res. 2016, 9, 2852. (42) Wallentin, J.; Wilke, R. N.; Osterhoff, M.; Salditt, T. Simultaneous high-resolution scanning Bragg contrast and ptychographic imaging of a single solar cell nanowire. J. Appl. Crystallogr. 2015, 48, 6, 1818-1826. (43) Wallentin, J.; Poncela, L. B.; Jansson, A. M.; Mergenthaler, K.; Ek, M.; Jacobsson, D.; Wallenberg, L. R.; Deppert, K.; Samuelson, L.; Hessman, D.; Borgström, M. T. Single GaInP nanowire p-i-n junctions near the direct to indirect bandgap crossover point. Appl. Phys. Lett. 2012, 100, 25, 251103-4. (44) Berg, A.; Lenrick, F.; Vainorious, N.; Beech, J. P.; Wallenberg, R. L.; Borgström, M. T. Growth parameter design for homogeneous material composition in ternary Ga x In 1− x P nanowires. Nanotechnology 2015, 26, 43, 435601. (45) Wu, J.; Borg, B. M.; Jacobsson, D.; Dick, K. A.; Wernersson, L.-E. Control of composition and morphology in InGaAs nanowires grown by metalorganic vapor phase epitaxy. J. Cryst. Growth 2013, 383, 158-165. (46) Amira, S. A.; Fonseka, H. A.; Philippe, C.; Jennifer, W.-L.; Roy, L. M. O. h. V.; Jessica, L. B.; Michael, B. J.; Hark Hoe, T.; Chennupati, J. In x Ga 1− x As nanowires with uniform composition, pure wurtzite crystal phase and taper-free morphology. Nanotechnology 2015, 26, 20, 205604.


22

Page 23 of 29

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(47) Kriegner, D.; Persson, J. M.; Etzelstorfer, T.; Jacobsson, D.; Wallentin, J.; Wagner, J. B.; Deppert, K.; Borgström, M. T.; Stangl, J. Structural investigation of GaInP nanowires using Xray diffraction. Thin Solid Films 2013, 543, 100–105. (48) Scott, S. A.; Lagally, M. G. Elastically strain-sharing nanomembranes: flexible and transferable strained silicon and silicon–germanium alloys. J. Phys. D: Appl. Phys. 2007, 40, 4, R75. (49) Nagai, H. Structure of vapor‐deposited GaxIn1−xAs crystals. J. Appl. Phys. 1974, 45, 9, 3789-3794. (50) Igarashi, O. Crystallographic Orientations and Interfacial Mismatches of Single‐Crystal CdS Films Deposited on Various Faces of Zinc‐Blende‐Type Materials. J. Appl. Phys. 1971, 42, 10, 4035-4043. (51) Ayers, J. E.; Ghandhi, S. K.; Schowalter, L. J. Crystallographic tilting of heteroepitaxial layers. J. Cryst. Growth 1991, 113, 3–4, 430-440. (52) Döring, F.; Robisch, A. L.; Eberl, C.; Osterhoff, M.; Ruhlandt, A.; Liese, T.; Schlenkrich, F.; Hoffmann, S.; Bartels, M.; Salditt, T.; Krebs, H. U. Sub-5 nm hard x-ray point focusing by a combined Kirkpatrick-Baez mirror and multilayer zone plate. Opt. Express 2013, 21, 16, 1931119323. (53) Pfeifer, M. A.; Williams, G. J.; Vartanyants, I. A.; Harder, R.; Robinson, I. K. Threedimensional mapping of a deformation field inside a nanocrystal. Nature 2006, 442, 7098, 63-66. (54) Godard, P.; Carbone, G.; Allain, M.; Mastropietro, F.; Chen, G.; Capello, L.; Diaz, A.; Metzger, T. H.; Stangl, J.; Chamard, V. Three-dimensional high-resolution quantitative microscopy of extended crystals. Nat. Comm. 2011, 2, 568.


23

Nano Letters

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

TOC GRAPHIC


24

GaAs substrate

III

1 um

Si3N4

Nano Letters C) I Meas. Shell Core

GaAs core

1 2 3 4 5 6 7 8 9

B)

II (011) ACS Paragon Plus Environment

|q| (1/Å)

D) GaAs

Page 25 of 29 GaInP A)

Nano Letters

A) 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 32 33 34

0.5 μm B)

Top

Base

C)


Page 26 of 29

Page 27 of 29

A)

Nano Letters

C)

D)

D)

log10(cts)

Nanowire X-ray Bragg diffraction qz

qy qx

|q| (1/Å) F)

E)

z (μm)

Along x

Along y

G)

Along z

0.3283

d111(nm) 0.3276

1 μm

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 32

B)

40 x (nm) y (nm)


A)

log10(cts)

Page 28 of 29

d111 (nm)

0.3276

4

B)

|q| (1/Å) C)

D) Along x-axis

qz

Along z-axis

z (μm)

0.3288

y (nm)

qy

z (μm)

θ qx

Along y-axis

qshell z (μm)

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 32 33 34 35

0.3290

Nano Letters

d111 (nm) 0.3276

φ y (nm)


x (nm)

x (nm)

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

Nano Letters

Nanowire X-ray

z (nm)

Page 29 of 29

0.3283

d111(nm) 0.3276

x (nm) y (nm)


Bending and Twisting Lattice Tilt in Strained CoreâShell Nanowires

Recommend Documents

Bending and Twisting Lattice Tilt in Strained CoreâShell Nanowires