Supporting Information. Polar Second-Harmonic Imaging to Resolve Pure. and Mixed Crystal Phases along GaAs Nanowires.

Transcription

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

2 Contents 1. Crystal structure characterization of the GaAs NWs with STEM and HRTEM Spectral measurements of GaAs NWs Theoretical analysis of the polarization-dependent SHG for WZ and ZB crystal phases in GaAs NWs Polarization-dependent SHG imaging of GaAs nanowires References Crystal structure characterization of the GaAs NWs with STEM and HRTEM The characterization of the GaAs NWs crystal structure was performed together with scanning transmission electron (STEM) and high-resolution transmission electron microscopies (HRTEM). The STEM measurements were taken in a scanning-electron microscopy (SEM) machine, modified with a transmission electron detector. The STEM images (Figure S1(a)) allow to study crystal structures in large areas of the NW at once. The contrast analysis of the images together with precise HRTEM studies of the same areas along the NW allows us to distinguish zones with different crystal structures inside the NW: zinc blende (ZB), wurtzite (WZ) and zones with mixed crystal structures, consist of WZ/ZB transitions or ZB rotational twins. Figure S1(a) displays the STEM image of the GaAs NW consisting of few small areas with different crystal structures. Figure S1(b) shows the HRTEM image of the same area of the NW. Figures S1(c-d) demonstrate the HRTEM images with corresponding FFT analysis of a close view of the WZ and ZB areas. Figures S1(c) Figure S1(d) confirm, that studied areas have ZB and WZ crystal structures respectively. 2

3 TEM grid (a) WZ ZB WZ (b) ZB WZ 200 nm 100 nm WZ twins (c) (d) 0.32 nm nm Figure S1. (a) STEM image of GaAs NWs, on Si3N4 TEM grid; (b) TEM image of the same area of the NW; (c-d) HRTEM image with FFT analysis of the close view (c) area with ZB crystal structure (d) area with WZ crystal structures. The STEM analysis together HRTEM show that zones with randomly switching defects inside NW are the ZB rotational twins, where two ZB crystal phases rotated one to each other. To determine the rotational twins inside mixed crystal structure we performed HRTEM measurements together with Selected Area Electron Diffraction (SAED) studies. Figure S2 demonstrates the HRTEM image with FFT analysis of the area with to two ZB crystal structures rotated one to each other and corresponding SAED images. 3

4 ZB twin plane (a) NW growth direction [111] (b) 1.5 nm Figure S2. (a) HRTEM image of the area with ZB rotation twins with corresponding FFT images for each ZB structure in ZB twin, (b) SAED image of the area with ZB rotation twins. Thus, if we compare the STEM measurements (Figure S1(a)) with HRTEM and FFT images (Figures S1(b-e)) from the same areas, we can conclude, that long areas of NW1 (Figure 1(c-d) in the manuscript) with bright contrast correspond to ZB crystal structure and areas with dark contrast correspond to WZ structure. HRTEM analysis together with SAED demonstrate, that except these zones we can distinguish areas with rotational twins inside NWs (Figure S1(b) and S2). We should notice, that the crystallographic planes of the WZ structures are tilted to the longitudinal axis of the NW. Indeed, some NWs were grown not perfectly perpendicular to the Si(111) substrate. The orientation of the crystal structure was misaligned to the growth direction of the NW and thereby c -axis is tilted to the NWs longitudinal axis (Figure S1(e)). 2. Spectral measurements of GaAs NWs Spectral measurements were carried out with an imaging spectrometer to record the fundamental and the second-harmonic responses of GaAs NWs The fundamental central wavelength of the incident laser was 820 nm. The schematic of the experimental setup is presented on the Figure 4

5 S3(a) 1. The intensity of the pumping laser beam was adjusted by combining a half-wave plate and a polarizing beam splitter. The polarization direction was controlled by an additional halfwave plate. The measured spectrum is presented on the Figure S3(b). Excitation laser beam was filtered out with BG39 filter but as it is much stronger than the SHG, it is still possible to see the 820 nm signal on Figure S3(b). The measured signal spectrum demonstrates a strong peak at 410 nm, the SHG signal, and no other peaks from defect-related luminescence emission, except the pump at 820 nm. (a) (b) GaAs SHG peak (410 nm) Laser (820 nm) Figure S3. (a) Schematic image of the optical setup for measuring SHG response with spectrometer, (b) the spectrum of transmitted SHG signal and corresponding pumping laser. The intensity of pumping laser was attenuated by a BG39 filter. 5

6 3. Theoretical analysis of the polarization-dependent SHG for WZ and ZB crystal phases in GaAs NWs To calculate the SHG responses we have to know the direction of the electric field E (ω) in the crystallographic frame (x c, y c, z c ), but the experiment is done in the laboratory frame (x, y, z). The pumping laser propagates along the z axis in laboratory frame, whereas the NWs are placed in the xy-plane. The electric field of the linearly polarized pumping laser has a controllably variable angle φ to determine the rotation of the polarization of the incoming laser in the laboratory frame. Figure S4 illustrates the geometry of the crystallographic frame orientation to the laboratory frame, where (α, β, γ) are Euler angles (Figure S4(b)). The position of the NWs crystallographic frame in laboratory coordinate system is determined by the rotation the (x c, y c, z c ) by angles (α, β, γ). Figure S4. (a) geometry of the laboratory (x, y, z) and crystallographic (x c, y c, z c ) frames. The linearly polarized pumping laser propagates along the z axis; the optical electric field of the pumping laser is in the xy-plane with variable angle φ, (b) geometry of the rotation crystallographic frame to the laboratory frame. 6

7 In general case, we assume, that the studied NW consists of a mixture between two monocrystalline phases I and II. For each monocrystalline phase we have to determine the electric field orientation E I (ω) and E II (ω) in the crystallographic frame. Using the rotation Euler matrix, we can present these the electric fields: E I,IIx (ω) E(ω) sin θ cos φ E I,II (ω) = ( E I,IIy (ω)) = R(α I,II, β I,II, γ I,II ) ( E(ω) sin θ sin φ), E I,IIz (ω) E(ω) cos θ (S1) where E(ω) is the electric field of the pumping laser, rotating in xy-plane in the laboratory coordinate system, φ the polarization rotational angle and R(α, β, γ) the rotation Euler matrixes: R(α, β, γ) = (S2) cos α cos β cos γ sin α sin γ cos γ sin α cos α cos β sin γ cos α sin β ( cos β cos γ sin α + cos α sin γ cos α cos γ cos β sin α sin γ sin α sin β), cos γ sin β sin β sin γ cos β where indexes I and II correspond to ZB or WZ structure, R ZB = R(α ZB, β ZB, γ ZB ) and R WZ = R(α WZ, β WZ, γ WZ ). The equation for the polarization at the doubled frequency P (2ω) is: P I,IIx (2ω) P I,II (2ω) = ( P I,IIy (2ω)) = P I,IIz (2ω) R 1 (2) (α I,II, β I,II, γ I,II ) 2χ I,II E 2 I,IIx (ω) E 2 I,IIy (ω) E 2 I,IIz (ω) 2 E I,IIy (ω)e I,IIz (ω), 2 E I,IIx (ω)e I,IIz (ω) ( 2 E I,IIx (ω)e I,IIy (ω) ) (S3) 7

8 R 1 (α I,II, β I,II, γ I,II ) is the inverse Euler matrix, that describe the inverse transition from (2) crystallographic coordinate system back to laboratorian, where we are measuring SHG, the χ I,II nonlinear second-order susceptibility tensors with components {d i,j } ({i, j} = 1,2,3,4,5,6). The (2) χ I,II tensors for WZ and ZB crystal structures have different nonzero components, which are depend on the classes of point group for these crystal structures. The ZB crystal structure belongs to 4 3m class of point group 2 and {d i,j } ZB will have nonzero components for (i = 1,2,3 and j = 4,5,6), where d 14 = d 25 = d 36 : (2) = {di,j } ZB = ( χ ZB d d d 36 ) (S4) The WZ GaAs, which has 6 mm class of point group {d i,j } WZ will have nonzero components for (i = 1,2,3 and j = 1,2,3,4,5,6), where d 15 = d 24, d 31 = d 32 3 : χ (2) WZ = {d i,j } WZ = ( d 31 d 31 d 33 0 d 15 0 d ) (S5) P I (2ω) and P II (2ω) corresponds to SHG responses from each monocrystalline phase (WZ or ZB). Thus, the overall response is as a linear combination of P I (2ω) and P II (2ω), according to (S3): P x (2ω) P Ix (2ω) P IIx (2ω) P (2ω) = ( P y (2ω)) = a ( P Iy (2ω)) + (1 a) ( P IIy (2ω)), P z (2ω) P Iz (2ω) P IIz (2ω) (S6) here a is the ratio between monocrystalline phases. Zone with pure phase is a particular case of our model with a = 1. For example, for pure WZ P (2ω) = P I (2ω) = P WZ (2ω), and for pure ZB P (2ω) = P I (2ω) = P ZB (2ω). For zone with ZB rotational twin defects, P I (2ω) and P II (2ω) are 8

9 SHG responses for each ZB rotation, and a defines ration between each ZB structures in studied area. The measured SHG response P SHG (2ω) can be expressed as: P SHG (2ω) = k P (2ω), (S7) here k normalizing coefficient for the estimation SHG collection efficiency, depending of the components of the experimental setup, such as: objectives, lenses, parameters of CCD detector, etc. 4. Polarization-dependent SHG imaging of GaAs nanowires The SHG images were recorded for polarizations of incident pump beam from 0º to 360º with steps of 10º on an EMCCD camera (animation with 36 SHG images available in supplementary movie). For the analysis of experimental results, all were firstly rotated and aligned to each other in order to correct matching of SHG responses in each pixel. Figure S5 presents examples of measured SHG responses for different incoming polarizations from parallel to perpendicular directions to the longitudinal axis of the NW with step 20º. Pol 0º Pol 20º Pol 40º Pol 60º Pol 80º Pol 90º Figure S5. Images of measured SHG responses from GaAs NW for different polarizations from 0º to 90º, with step 20º. From each image of SHG responses we got profiles of SHG intensities. Figure S6 presents the examples the profiles of SHG intensities in NW s longitudinal direction for 0º and 90º polarization (Figure S5) of incoming laser excitation. 9

10 Figure S6. Profiles of SHG intensities in NW longitudinal direction. 5. References (1) Grange, R.; Brönstrup, G.; Kiometzis, M.; Sergeyev, A.; Richter, J.; Leiterer, C.; Fritzsche, W.; Gutsche, C.; Lysov, A.; Prost, W.; Tegude, F.; Pertsch, T.; Tu, A.; Christiansen, S. Nano Lett. 2012, 12 (10), (2) Boyd, R. Y. Nonlinear Optics, 3rd ed.; Academic Press is an imprint of Elsevier: The Institute of Optics University of Rochester Rochester, New York USA, (3) Chen, R.; Crankshaw, S.; Tran, T.; Chuang, L. C.; Moewe, M.; Chang-Hasnain, C. Appl. Phys. Lett. 2010, 96 (5),