Polar Second-Harmonic Imaging to Resolve Pure ... - ACS Publications

Letter pubs.acs.org/NanoLett

Polar Second-Harmonic Imaging to Resolve Pure and Mixed Crystal Phases along GaAs Nanowires Maria Timofeeva,*,†,§ Alexei Bouravleuv,‡,∥ George Cirlin,‡,§,∥ Igor Shtrom,‡,∥ Ilya Soshnikov,‡,∥ Marc Reig Escalé,† Anton Sergeyev,† and Rachel Grange*,† †

Optical Nanomaterial Group, Institute for Quantum Electronics, Department of Physics, ETH Zurich, Auguste-Piccard Hof 1, 8093 Zurich, Switzerland ‡ St. Petersburg Academic University, Khlopina 8/3, 194021 Saint Petersburg, Russia § ITMO University, Kronverkskiy 49, 197101 Saint Petersburg, Russia ∥ Ioffe Institute, Politekhnicheskaya 29, 194021 Saint Petersburg, Russia S Supporting Information *

ABSTRACT: In this work, we report an optical method for characterizing crystal phases along single-semiconductor III−V nanowires based on the measurement of polarization-dependent second-harmonic generation. This powerful imaging method is based on a per-pixel analysis of the second-harmonic-generated signal on the incoming excitation polarization. The dependence of the second-harmonic generation responses on the nonlinear second-order susceptibility tensor allows the distinguishing of areas of pure wurtzite, zinc blende, and mixed and rotational twins crystal structures in individual nanowires. With a far-field nonlinear optical microscope, we recorded the second-harmonic generation in GaAs nanowires and precisely determined their various crystal structures by analyzing the polar response for each pixel of the images. The predicted crystal phases in GaAs nanowire are confirmed with scanning transmission electron and high-resolution transmission electron measurements. The developed method of analyzing the nonlinear polar response of each pixel can be used for an investigation of nanowire crystal structure that is quick, sensitive to structural transitions, nondestructive, and on-the-spot. It can be applied for the crystal phase characterization of nanowires built into optoelectronic devices in which electron microscopy cannot be performed (for example, in lab-on-a-chip devices). Moreover, this method is not limited to GaAs nanowires but can be used for other nonlinear optical nanostructures. KEYWORDS: Nanowires, second-harmonic generation, polar second-harmonic imaging, GaAs, wurtzite, zinc blende, twins, crystal phase, far-field microscopy, polarization-dependent, scanning electron microscopy, high-resolution transmission electron microscopy

S

During the NW growth, the crystal phases can be switched between ZB and WZ phases by varying the flux ratio or growth temperature.17,23,24 These properties expand the range of potential III-V NWs applications. For instance, pure WZ GaAs NWs can be used as components for piezoelectronic devices25 and WZ−ZB heterostructures in InAs NWs can be used as single-electron devices.17,26 Transmission electron microscopy (TEM) is one of the most powerful techniques for characterizing crystal structures of nanomaterials, but it requires placing the NWs on ultrathin substrates. Consequently, TEM cannot be used for nondestructive crystal structure analysis of NWs, which are already implemented inside an optoelectronic system, such as lab-on-a-chip devices or arrays of nanotransistors.27,28 Therefore, there is a need for the development

emiconductor nanowires (NWs) have attracted a lot of research interest due to their unique optical and electronic properties.1−3 For example, they are used in band-gap engineering by combining different III−V materials into a single NW structure.1 Therefore, NWs are one of the main building blocks for the new generation of nanophotonic devices, such as photodetectors,4,5 solar cells,6 lasers,7,8 and sensors.9 One of the unique features of the NWs is the possibility of engineering crystallographic phases that typically cannot be fabricated at normal conditions in bulk III−V semiconductor materials. For example, it is possible to grow III−V NWs with pure wurtzite (WZ), pure zinc blende (ZB), mixed WZ−ZB crystal phases, or with ZB rotational twins.10,11 Recent experimental and theoretical studies show that WZ and ZB gallium arsenide (GaAs)12−16 and indium arsenide (InAs)17−19 NWs have different band gaps. Thus, the control of the growth parameters20,21 allows the fabrication of WZ−ZB heterostructures based on the same semiconductor material22 (for example, on GaAs16,23 or indium arsenide (InAs)).17,19 © 2016 American Chemical Society

Received: June 23, 2016 Revised: September 2, 2016 Published: September 22, 2016 6290

DOI: 10.1021/acs.nanolett.6b02592 Nano Lett. 2016, 16, 6290−6297

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sensitive to the crystal structure transitions technique for characterization of NW crystal phases at standard room conditions and even within optoelectronic devices. The studied GaAs NWs were grown by the molecular-beam epitaxy (MBE) technique with gold as a catalyst on Si (111) substrate. Growth conditions (see the Methods section) allowed us to get NWs with multiple elongated areas of pure WZ, ZB, mixed WZ−ZB crystal phases, and rotational twins. Figure 1a presents the scanning electron microscopy (SEM) image of GaAs NWs, grown on a Si (111) substrate. To compare the performance of electron microscopy and polar SHG imaging methods, we perform both measurements on the same NW. We mechanically transfer the NWs onto a copper grid with a 50 nm silicon nitride (Si3N4) thin film that can be placed either in electron or in optical microscopes.46 First, we present the study of the crystal structure of NW with scanning transmission electron (STEM) and high-resolution transmission electron (HRTEM) microscopies. Figure 1b shows the STEM image of one of the studied NWs on a Si3N4 TEM film that is later referred as NW1. The contrast on the STEM image (Figure 1c) shows that NW1 consists of four zones (numbered I−IV) with different crystal structures. Figure 1d shows the STEM image of the Zone I and Zone II at a higher magnification that on the Figure 1c. The variations of contrast in the gray scale demonstrate the differences of the Zone I and Zone II; note that there is a Si3N4 film defect, confirmed with HRTEM imaging. Panels e and f of Figure 1 present the HRTEM images of the Zones II, III (partly) and IV, respectively. The HRTEM and fast Fourier transform (FFT) analysis in Figure 1e demonstrates that Zone II has a ZB crystal phase with randomly switching crystal structure, which is typical for rotational ZB twins.11 The Figure 1f shows the differences in crystal structure in Zones III and IV. To unambiguously confirm the corresponding crystal structures within the studied NW1, we present the STEM and HRTEM images with selected area electron diffraction (SAED) analysis of the ZB and WZ on Figure 2a−f. To obtain highquality images, we chose the another GaAs NW from the same experimental sample with the same STEM contrast profiles of the pure WZ and ZB crystal structures as NW1. Therefore, the presented results of STEM and HRTEM with SAED and FFT analyses (Figures 1 and 2) show that the NW1 consists of four zones with different types of crystal structures: Zone I, pure WZ; Zone II, rotational twins; Zone III, pure ZB; and Zone IV, WZ (detailed in Figures S1 and S2). The nonlinear optical characterization of the GaAs NWs was performed by recording the SHG response from different areas of NW1 (Figure 1b,c) at different polarizations of the incident laser. The SHG response P⃗ (2ω) depends on the polarization of the incident electric field E⃗ (ω) and the nonlinear second-order susceptibility tensor χ(2):

of new noninvasive investigation methods to study NW crystal structure. Several research groups are focused on the development of different techniques for crystal phase investigations; the main ones are micro- and nanophotoluminescence,29,30 Raman spectroscopy,31,32 and cathodoluminescence.33 Despite the fact that these methods are widely used, they have some environment and sensitivity limitations. For example, microphotoluminescence requires liquid helium temperature.12,34 Raman spectroscopy has a sensitivity limitation to the structural transitions and rotations inside NWs.35 In addition, cathodoluminescence requires a low-temperature environment and scanning to perform the measurement.33 These limitations motivated us to propose a novel far-field room temperature imaging technique based on nonlinear optical microscopy with polarization resolution down to single pixels to differentiate pure and mixed crystal structures in NWs. Recently, the nonlinear optical processes in III−V NWs, like second-harmonic generation (SHG)36−39 or four-wave mixing,40 have attracted a lot of interest for their possible applications in nonlinear optical devices. The SHG is the second-order nonlinear optical process, in which two photons with a fundamental angular frequency (ω) are converted into one photon with an angular frequency (2ω). The SHG is sensitive to crystallographic symmetry changes that makes the SHG polarimetry a very promising technique for studying crystal structure and orientation in different types of nonlinear materials. Polarization-dependent SHG is effectively used for investigations of the nonlinear optical properties and different crystal structure symmetries in III−V materials, such as GaAs,38,39,41 InAs,42 and GaN.43 Previous studies demonstrate highly efficient SHG in different types of semiconductor NWs, such as ZnO,44 ZnTe,45 CdS,46 ZnS,47 GaAs,36,37,48,49 and GaP.50 Some recent studies use polarizationdependent SHG measurements for the crystallographic characterization of GaN,43 ZnO,51 CdS,46 ZnS,47 and, ZnSe52 NWs. Until now, polarization-dependent SHG measurements were mostly implemented to determine crystal lattice orientations and phases in NWs with the same crystal structure along the NW length.46,47 In this work, we present an optical method for distinguishing areas with different crystal phases within single NWs. This approach is based on a nonscanning multiphoton imaging with a wide-area illumination36 and per-pixel analysis of SHG images obtained for different incoming excitation polarizations. We apply this optical method to study GaAs NWs that contain different crystal structures, which is typical in GaAs NW growth.53 We demonstrate that we can precisely distinguish areas with pure WZ, pure ZB, mixed crystal phases, and rotated ZB crystal lattices, also called rotational twins, along individual NWs. It is well-known that the SHG response depends on the polarization of the incoming laser light. This dependence occurs due to the nonlinear properties of the material that are determined by the second-order susceptibility tensor χ(2). The components of the χ(2) tensor are defined by crystallographic point groups, and they are different for ZB and WZ crystal structures.54 Per-pixel analysis of the images and the corresponding shapes of polar SHG responses allow the unambiguous resolution of areas with different crystal phases within single NWs. With this nonlinear polar microscope technique, we can overcome the limitations of the electron microscopy or optical methods, such as the necessity to transfer NWs on the TEM grids or to use a low-temperature environment, which is needed for photoluminescence measurements. Thus, the developed imaging method is promising as an alternative nondestructive, being

⃗ ω) ∝ χ (2) ·E ⃗(ω) ·E ⃗(ω) P (2

(1)

The components and shapes of the χ tensors depend on the type of the crystallographic point group in the material. The ZB areas belong to the 4̅3m point group,54 and the WZ crystal structure in GaAs NWs belong to the 6 mm crystallographic point group37 (eq 4). Because each class of point group has different χ(2) components, its SHG response will be different. Therefore, the analysis of the polarization-dependent SHG responses allows us to distinguish WZ, ZB, twins, and areas with mixed structures along a single GaAs NW. The experimental studies of the polarization-dependent SHG in GaAs NWs were carried out with a home-built transmission (2)

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Figure 1. (a) SEM image of the GaAs NWs on Si, as grown on Si substrate. (b) STEM image of GaAs NWs transferred on 50 nm Si3N4 TEM film. (c) STEM image of NW1. (d) STEM with higher magnification of Zone I and Zone II. (e,f) HRTEM images of different zones in NW1: (e) Zone II with corresponding FFT patterns and (f) part of Zone III and Zone IV.

SHG response of the GaAs NW was measured by rotation of the pumping laser with HW2. As shown in Figure 3b, the laser propagates along the z-axis in the laboratory frame, whereas the NW lies in the xy plane. Angle φ determines the rotation of the incoming polarization. Zoomed-out insertion (Figure 3a) demonstrates that the laser beam excites the whole NW at the same time. Figure 3b illustrates the geometry of the laboratory frame (x,y,z) and the crystallographic frame (xc,yc,zc), which might not be aligned with longitudinal axis of the NW. To perform the polarization-dependent SHG measurements with NW1 (Figure 1c), we recorded images of the SHG intensities by varying the polarization of the incident pump beam from 0° to 360° with steps of 10° (animation with 36 SHG images available as a supplementary movie). For each polarization, we recorded a single SHG image. Figure 4a,b shows the example of two normalized SHG images of the NW1 illuminated with the electric field of the laser beam perpendicular and parallel to the NW longitudinal axis. For each single SHG image, we extracted the intensity profiles along the NW (Figure S5). Analysis of the SHG intensity profiles for each polarization allows us to display the polar plots of the SHG intensity as a function of the polarization

microscope system (Figure 3a) at room temperature and in an air environment.36 For the SHG microscopy, a pulsed laser beam from a Ti−sapphire oscillator was focused with a 10× objective down to 5 μm in diameter to illuminate a large area without requiring scanning of the incident light.36,55 The central wavelength of the incident laser was 820 nm, the pulse duration was around 100 fs at the laser beam output, the repetition rate was 80 MHz, and the average power was 3.5 mW. Figure 3a presents a schematic of the experimental setup for polarization-dependent SHG imaging. The intensity of the pumping laser beam was adjusted by combining a half-wave plate (HW1) and a polarizing beam splitter (BS). The polarization was controlled by an additional half-wave plate (HW2). The NW was placed in the focal plane of the incident laser beam. The SHG signal was collected with a 100× objective (numerical aperture 0.8) and imaged with the 250 mm lens onto a cooled (−70 °C) electron-multiplying charge-coupled device (EMCCD) camera with low-pass filters to cut the pump laser signal. Moreover, the SHG signal was collected with a spectrometer, to confirm the frequency doubling of the pumping laser (spectrum and setup in Figure S3b). The polarization-dependent 6292

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Figure 2. (a) STEM and (b−d) corresponding SAED diffraction images for the area with (b) ZB, (c) intersection between WZ and ZB, and (d) WZ crystal structures. (e,f) Corresponding HRTEM images of (e) WZ and (f) ZB crystal structures.

Figure 3. (a) Schematic of the wide-illumination optical setup for polarization measurements of SHG from GaAs NWs. (b) Geometry of the laboratory frame (x,y,z) and crystallographic frame (xc,yc,zc) rotated to the laboratory frame with the linearly polarized pumping laser propagates along the z axis; the optical electric field of the pumping laser is in the xy plane with the variable angle φ.

angle φ for each pixel on the SHG image. We split the NW into zones with similar polar plots. The variations of the shapes of the polar plots along the zones allow us to determine the crystal structure transitions within the single GaAs NW. Figure 4c shows the SHG polar plots for Zones I (circles) and III (squares) (Figure 1c), where φ is corresponding polarization angle (see also Figure 3b). The polar plot of the SHG response from the Zone I has a shape with two symmetrical lobes (dipole shape). The SHG response from the Zone III has a shape with four lobes (quadrupole shape). To perform the per-pixel analysis, all images were aligned to each other to suppress the results of drifts and vibrations during SHG measurements. On each SHG image (Figure 4a,b), there is also a periodic pattern resulting from the interference between the fundamental mode of a guided wave modulating the Mie-scattered incident light, demonstrated in previous work.36 We developed a theoretical model to calculate the polarization-dependent SHG responses for arbitrary mixture of WZ and ZB crystal phases with variable rotations (detailed calculations are shown in eqs S1−S7). This model was used to fit the experimental results of the SHG response from each zone (Figure 5). Furthermore, it allowed us to determine the position within the NW, where changes of phases occur, and estimate the ratio between the monocrystalline phases for the mixed areas. The SHG response from an area with pure crystal phase is defined by the χ(2) tensor in the corresponding crystallographic frame (xc,yc,zc) orientation. In general case this orientation is

unknown. In the laboratory frame (Figure 3b) for a given electric field direction E⃗ (ω), the SHG response P⃗ (2ω) can be calculated by transforming the electric field direction E⃗ (ω) to the crystallographic frame first, evaluating eq 1 in this frame, and then converting the SHG response vector back to the laboratory frame (x,y,z) using the inverse transformation. These transformations are defined by Euler rotation matrices (eq S2) with angles used as parameters in our model. In our model, we are considering the general case in which the studied area consists of a mixture between two monocrystalline phases. Assuming that P⃗ I(2ω) and P⃗II(2ω) are the SHG responses from each monocrystalline phase, WZ and ZB, respectively, we can express the overall response as a linear combination of P⃗I(2ω) and P⃗ II(2ω): ⃗ ω) = aPI⃗ (2ω) + (1 − a)PII⃗ (2ω) P (2

(2)

where a is the ratio between monocrystalline phases. The zone with a pure phase is a particular case of our model with a = 1. For example, for pure WZ, P⃗(2ω) = P⃗ I(2ω) = P⃗ WZ(2ω), and for pure ZB, P⃗ (2ω) = P⃗ I(2ω) = P⃗ZB(2ω). For zones with rotational twin defects, P⃗I(2ω) and P⃗II(2ω) are SHG responses for each ZB rotation, and a defines the ratio between each ZB structure. The measured SHG response PSHG(2ω) can be expressed as ⃗ ω)| PSHG(2ω) = k|P (2

(3)

where k is a normalizing coefficient for the SHG collection efficiency, which depends on the components of the 6293

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Figure 4. SHG images of the GaAs NW1 with (a) parallel and (b) perpendicular incoming laser beam polarization (Zones I−IV of the studied areas of the NW1 are highlighted). (c) Polar plots for SHG signals from Zones I (circles) and III (squares) connected with lines to guide the eye. The NW is shown in yellow.

experimental setup, such as objectives, lenses, parameters of EMCCD, etc. In eq 3, the SHG intensity depends on the E⃗ (ω) direction and the crystal structure orientation. Panels a, c, e, and g of Figure 5 present the 3D visualizations of the SHG responses for each possible crystal structure and for every direction of E⃗ (ω), where (x,y,z) axes correspond to laboratory frame (Figure 3b) and φ − polarization angle. The shapes of these 3D surfaces are defined by the components of the χ(2) tensors. As we mentioned, ZB and WZ GaAs belongs to 43̅ m and 6 mm classes of point groups, respectively. Thus, the χ(2) tensors for WZ and ZB phases are (2) χZB

(2) χWZ

⎛ 0 0 0 d36 0 0 ⎞ ⎜ ⎟ = ⎜ 0 0 0 0 d36 0 ⎟ ⎜⎜ ⎟⎟ ⎝ 0 0 0 0 0 d36 ⎠ ⎛ 0 0 0 0 d15 0 ⎞ ⎜ ⎟ = ⎜ 0 0 0 d15 0 0 ⎟ ⎜⎜ ⎟⎟ ⎝ d31 d31 d33 0 0 0 ⎠

Figure 5. Theoretical and experimental SHG responses of the NW1 (Figure 1c). On the 3D polar plots, cross-sectional planes (blue curves) correspond to the theoretical (solid lines) and experimental (dots) SHG responses for the zones: (a,b) Zone I; (c,d) Zone II; (e,f) Zone III, and (g,h) Zone IV, where (x,y,z) is the corresponding laboratory frame and φ is the corresponding polarization angle. (4)

The nonzero components of χ(2) ZB for GaAs are typically at 1064 nm: d14 = d25 = d36 = 370 pm/V.54 The WZ GaAs material is not so

can be explained by the differences of excitation wavelength and experimental parameters, such as the collection efficiency of the optical components, the EMCCD camera parameters, etc. In our experiment, the incident field E⃗ (ω) was varied in the xy plane, and the measured polar plots of SHG intensities correspond to one cross-section of the modeled 3D surfaces highlighted in each 3D plot of Figure 5. Panels b, d, f, and h in Figure 5 present the comparison of the measured (circles) and the

well-studied in terms of nonlinear susceptibility characteristics. Based on the recent work of R. Chen at al.,37 in our model, we used the following values for χ(2) WZ: d15 = d24 = 42 pm/V, d31 = d32 = 21 pm/V, and d33 = 115 pm/V, but for the components d15 and d31, the values were selected to be 15%−20% lower than the measured values in ref 37. These variations of nonlinear responses 6294

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structure (WZ or ZB) or periodical WZ−ZB heterostructures. Therefore, the presented far-field nonlinear optical measurements per pixel can reduce reliance on high-resolution electron microscopy for accelerating and simplifying crystal structure analysis. Methods. Nanowire Fabrication. The samples were grown by MBE using a Riber Compact 21 system equipped with an additional vacuum chamber for gold deposition. The growth experiments were carried out on epi-ready Si (111) substrates. First, Si (111) substrates were loaded into a vacuum chamber, where they were preliminarily outgassed at 800 °C before the gold deposition. Next, substrates were kept at 550 °C for 1 min to improve the droplet size homogeneity. The substrates were transferred to the main growth chamber with no vacuum brake. The GaAs NWs were grown at 600 °C for 30 min. The nanowire appearance was controlled by reflection high-energy diffraction (RHEED). STEM and HRTEM Characterization. The SEM and STEM characterizations were carried out in a Magellan FEI 400 with an additional transmission detector. Analysis of the contrast of the STEM images allows us to distinguish ZB and WZ crystal structures in the NW. The HRTEM studies were performed with TEM F30 FEI Tecnai and FEI Talos F200× (Figures S1 and S2) with 0.18 and 0.12 nm resolutions, respectively. Images from the HRTEM were analyzed with FFT methods to characterize the reflexes from ZB and WZ crystal phases in GaAs NWs. Nonlinear Optical Measurements. Nonlinear optical measurements were performed with a home-built nonscanning transmission optical microscope. The excitation light was a tunable laser (range 690−1040 nm). The laser light (820 nm) was focused with a 10× Olympus objective on the TEM film with the GaAs NWs. The signal was then collected with a 100× objective and focused onto an EMCCD camera to get SHG signal images. The laser light was filtered out with BG-39 filter (transmission range 300−700 nm). The power of the incoming light was controlled by a half-wave plate and a polarizing beam splitter, and an additional half-wave plate was used for changing the polarization of the excitation laser light. Spectral measurements (Figure S3) were carried out with a SpectraPro SP2300 imaging spectrometer from Princeton Instruments. Polarization-Dependent SHG Imaging. The SHG images were recorded for each polarization between 0° and 360° every 10°. The intensity of the SHG signal on each image was analyzed precisely in each pixel in the longitudinal direction of the NW. For the longitudinal analysis, all images were aligned to decrease the shifts of the SHG signal for each parts of the NW.

modeled (lines) polar SHG responses for zones I−IV for the GaAs NW1 (Figure 1c), and φ is the corresponding polarization angle. The presented method with per-pixel analysis of images with polarization-dependent SHG responses allows us to classify areas with different crystal structures inside NWs. Even though we record the SHG images with pixel size resolution equivalent to 55 nm, the spectra of the SHG responses have Gaussian shapes and overlap between neighborhood pixels (Figure S3b). Therefore, it reduces the resolution down to 200−300 nm. However, using the objectives with higher magnification and a more sensitive camera, we may increase the spatial resolution of this method. Theoretical 3D shapes for pure WZ (Figure 5a) and ZB (Figure 5e) have different cross-sections regardless of the cutting plane orientation. Cross-sections for ZB structures have quadrupole shapes, while WZ has dipole shapes. As presented in panels b and f of Figure 5, the measured SHG polar plots for Zone I and Zone III were successfully fitted with our theoretical model. By studying the shape variations of the SHG polar plots, we can unambiguously distinguish areas with WZ and ZB phases. The SHG polar plots for Zones II and III have a quadrupole shape (Figure 5d,f); therefore, we can assume that they consist of a ZB crystal structure. The STEM and HRTEM images (panels c and e of Figure 1) show that Zone II has randomly switching mixture of two ZB crystal phases, which is typical for rotational twins,11 with domination of one phase (dark areas in Zone II on Figure 1c). Thus, according to the contrast difference on the STEM image, Zone II mainly contains a ZB crystal structure (dark area on Figure 1c) that is a rotational twin for the ZB crystal phase in Zone III (brighter area). Thus, there is a rotation of the ZB crystal lattice between Zone II and Zone III, which can be clearly distinguished from the rotation of the measured SHG polar plots (panels d and f of Figure 5). Within Zone II, we can resolve the dominating crystal phase according to the bestmatching shape (Figure 5d) within the resolution limit of the method. Nevertheless, analysis of the rotation between SHG polar plots that have similar quadrupole shapes allows us to detect the rotation of ZB structures within the NW. The SHG polar plot for Zone IV (Figure 5h) has primarily a dipole shape but does not match the pure WZ as in Zone I (Figure 5b). However, it can be perfectly fitted as a WZ−ZB mixed structure. Our model allows us to estimate the ratio of each crystal structure, which is about 10% ZB and 90% WZ in Zone IV. In summary, we developed an optical nondestructive method, which is substrate-independent, for resolving pure, mixed crystal phases and rotational twins along NWs. The presented method was used to distinguish areas of pure WZ, ZB, rotational twins, and mixed WZ−ZB crystal phases in GaAs NWs grown by MBE. For mixed WZ−ZB crystal phases, this method allows us to estimate the ratio of WZ to ZB inside the structure. For the zones with similar SHG polar plot shapes, the rotation between these polar plots allows us to determine the rotation of the ZB crystal structure within the NW. The proposed 3D theoretical model of polar SHG responses perfectly fits the experimental results and demonstrates a very general way to evaluate a crystal structure by the χ(2) tensor of the material. Moreover, this model can be easily transferred to other materials if the components of the χ(2) tensor are known. The suggested method is flexible and can be applied to NWs without any special preparation and conditions, such as a vacuum or a low-temperature environment. The investigation of crystal phases in III−V NWs is critical for the fabrication of high-quality optoelectronic devices, which require a pure crystal

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b02592. Additional details on crystal structure characterization of the GaAs NWs with STEM and HRTEM, spectral measurements of GaAs NWs, and a theoretical analysis of the polarization-dependent SHG for WZ and ZB crystal phases in GaAs NWs. Figures showing STEM, TEM, HRTEM, and SAED images of GaAs NWs; areas with crystal structures; schematic image of the optical setup for measuring SHG response with spectrometer; the spectrum of transmitted SHG signal and corresponding pumping laser; geometry of the laboratory and crystallographic 6295

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frames; polarization-dependent SHG imaging of GaAs nanowires; images of measured SHG responses from GaAs NW for different polarizations; and profiles of SHG intensities in NW longitudinal direction. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*M.T. e-mail: [email protected]. *R.G. e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Swiss Government Excellence Scholarships for Foreign Students and the Swiss National Science Foundation grant no. 150609. The samples were grown under support of Russian Science Foundation (14-12-00393). Furthermore, the authors acknowledge support of the Scientific Center for Optical and Electron Microscopy ScopeM of the Swiss Federal Institute of Technology ETHZ.

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ABBREVIATIONS NW, nanowires; MBE, molecular-beam epitaxy; SHG, secondharmonic generation; WZ, wurtzite; ZB, zinc blende; STEM, scanning transmission electron microscopy; HRTEM, highresolution transmission electron microscopy; EMCCD, electronmultiplying charge-coupled device

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