Deformed Honeycomb Lattices of InGaAs Nanowires Grown on Silicon‐on‐Insulator for Photonic Crystal Surface‐Emitting Lasers

Photonic crystals can be used to achieve high‐performance surface‐emitting lasers and enable novel photonic topological insulator devices. In this work, a GaAs/InGaAs heterojunction nanowire platform by selective area metalorganic vapor phase epitaxy for such applications is demonstrated. The nanowires are arranged into deformed honeycomb lattices on silicon‐on‐insulator substrate to exploit the quadrupolar photonic band‐edge mode. Core–shell and axial heterostructures are formed with their crystalline properties studied by scanning transmission electron microscopy. Room‐temperature, single mode lasing from both stretched and compressed honeycomb lattices within the telecom‐O band, with lasing threshold as low as 1.25 µJ cm−2 is demonstrated. The potential of using InGaAs nanowire‐based honeycomb lattices for small‐divergence surface‐emitting lasers and topological edge mode lasers is investigated. Finite‐difference time‐domain far field simulations suggest a sub‐10° beam divergence can be achieved thanks to the out‐of‐plane diffraction.


Introduction
Recent developments in photonic crystal (PhC)-based lasers have demonstrated superior performance to commonly used vertical cavity surface-emitting lasers (VCSELs) and edge emitting lasers. [1][2][3][4] The single-mode operation, high modulation frequency and brightness, [5,6] and symmetric beam profiles with In this work, we demonstrate GaAs/InGaAs nanowires selectively grown on SOI substrate as a material platform for surface-emitting telecom lasers and potential topological cavity lasers. In contrast to a square lattice which uses off-Γ symmetry points, [15,23] these nanowires are arranged into deformed honeycomb lattices to access Γ point band edge modes for highly directional vertical emission. Our fully integrated, bottomup approach allows to completely define the geometry of the system through control of the growth parameters and to achieve atomically smooth side facets, minimizing light scattering in the cavity. We experimentally demonstrate that lasing occurs at the Γ point band-edge of the honeycomb photonic band structures, with lasing wavelengths reaching the telecom O-band. With the aid of numerical simulations, we discuss the potential of employing these highly uniform, lithographically defined nanowire arrays for achieving small angle divergence PCSELs and designing novel topological cavity lasers.

Modeling and Growth
First, we consider a 2D PhC structure based on an ideal honeycomb lattice composed of core-shell GaAs/InGaAs/InGaP nanowires on an SOI substrate, as shown in Figure 1a,b. The honeycomb lattice can be obtained by placing hexagonal unit cells with side length R at the lattice sites of a hexagonal lattice defined by the basis vectors 1  a and 2  a and the lattice constant a given as | | | | 1 2   a a = (see Figure 1c). This PhC lattice natively presents a photonic band structure with a double Dirac cone, which is folded back from K and K′ points, at the Γ point in momentum space for transverse-magnetic (TM) modes. [24] This degeneracy can be lifted by stretching or compressing the edge length R = a/3, thereby preserving the hexagonal unit cell shapes so that the photonic bands exhibit characteristic electron p and d orbital-like electric field profiles. Here, we consider the stretched honeycomb lattice, with unit cells comprised of 12 InGaAs nanowires (n = 3.6) cladded between an SOI substrate and air. Photonic band structures and mode profiles were calculated using the guided mode expansion method [25] and confirmed via finite-difference time-domain (FDTD) simulations. We model the lattice parameters such that the bottom band-edge mode has a frequency at the Γ point matching the telecom O-band wavelength. With parameters of a = 640 nm and R = 230 nm, the bottom band-edge has a frequency of ω = 0.50 × 2πc/a (λ = 1280 nm) as shown in Figure 1d. It is also noted this band-edge mode presents a quadrupole mode, as indicated by the in-plane and cross-sectional electric field profiles in Figure 1e, resulting from the dipole and quadrupole band-inversion in the stretched honeycomb lattice. [9,24] The overlap of the quadrupole mode with the gain material is as high as 40%. Since the mode group velocity dω/dk vanishes at the band edge, the increased interaction time with the active gain material leads to gain enhancement. [1,26] The nanowires were grown using selective-area metalorganic vapor phase epitaxy (MOVPE). We started from a (111) SOI wafer with a thick buried oxide and a Si top layer which was thinned down to a nominal thickness of 40 nm for better optical confinement in the vertical direction. A 20 nm SiN layer was deposited using plasma-enhanced chemical vapor deposition as the growth mask. The substrate was patterned using electron-beam lithography and etched to expose the thin Si layer in circular nanoholes as small as 30 nm in diameter, as shown by a topview scanning electron microscopy (SEM) image in Figure 2a.
The nanoholes are arranged into ideal, stretched, and compressed honeycomb lattices. Prior to nanowire growth, the patterned substrate was cleaned using a diluted hydrofluoric acid solution to remove native oxide on the silicon surface and then transferred into the reactor chamber immediately. Annealing in the MOVPE reactor at a wafer surface temperature of 850 °C in hydrogen was carried out to desorb any residual oxide and prepare the silicon surface for III-V nucleation. The precursors used for nanowire growth are triethylgallium, trimethylindium, tertiarybutylarsine, and tertiarybutylphosphine. GaAs core nanowires were grown first from the Si surface at 680 °C under a V/III ratio of 82. The growth temperature was then reduced to 610 °C for growing InGaAs under a V/III ratio of 40 and an In/III vapor supply of 40%. We expect InGaAs will grow faster vertically with some lateral overgrowth surrounding the GaAs core, which is confirmed by transmission electron microscope (TEM) and will be discussed shortly. Finally, The GaAs/InGaAs nanowires were capped by 15 nm InGaP shells to reduce nonradiative surface recombination and improve the radiation efficiency. The reason of growing the GaAs stem is twofold. First, starting with a GaAs seeding layer significantly improves the yield and uniformity of nanowire growth on silicon. Second, the refractive index difference in the GaAs/InGaAs heterostructure improves optical confinement and mitigates optical field leakage into the silicon substrate.

Results and Discussion
After selective area epitaxy (SAE), we achieved ≈100% yield over nanowire arrays as large as 60 × 60 µm 2 with good uniformity. A tilted view SEM image of a 40 × 40 µm 2 nanowire array is displayed in Figure 2b, with a zoom-in image in Figure 2c showing atomically flat sidewalls along the {110} planes. Figure 2d shows a top-view SEM image of the nanowires indicating some variations of their hexagonal cross-sections. The measured height H and diameter d of the nanowires from SEM are 630 ±10 and 163 ± 8 nm, respectively. With increased nanohole diameter from 30 to 40 and 50 nm, the likelihood of neighboring nanowires merging into fin-like structures [27] increases by four and six times, respectively. We also noted the effect of different nanowire array sizes on the nanowire dimensions. For 40 × 40, 50 × 50, and 60 × 60 µm 2 arrays, there was a slight decrease in nanowire diameter from 176 to 170 to 163 nm, which we attribute to the group-III limited diffusion dynamics in SAE.
To confirm the material composition, thickness, and crystalline structure, we then performed high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and energy dispersive X-ray spectroscopy (EDX). This was done by breaking nanowires off the SOI substrate from the SiN mask openings and then placing the wires on the TEM graphene grid using a micromanipulator in an SEM. From the EDX mapping of Figure 3a, the GaAs core is with ≈80 nm diameter and 230 nm height. The InGaAs layer exhibits pronounced axial growth from the top (111)B facet of GaAs as well as considerable radial growth (≈45 nm) from the six side-faces, forming a coaxial core-shell structure at the bottom. The contrast in the EDX mapping suggests different indium incorporation in axial and radial growth. In catalyst-free SAE nanowires, growing core-shell structures with lattice mismatched materials often lead to shell nonuniformity or nanowire bending as a result of the Strankski−Krastanov (SK) 3D island growth mode induced by the misfit strain. [28][29][30][31] Here, we are able to achieve uniform growth of InGaAs shell around the GaAs core while maintaining the hexagonal nanowire morphology, which is further verified by the cross-sectional HAADF-STEM image taken from the nanowire base shown in Figure 3b. We believe the demonstrated strained GaAs/InGaAs heterostructure here can add additional flexibility in engineering nanowire heterojunction devices. From our simulation studies, the GaAs core of 230 nm height is beneficial in elevating the optical mode and mitigating light leakage to the Si device layer. Future work will follow to further increase the indium composition to extend emission wavelength into telecom C-band and embed strained InGaAs multi-quantumwell structures into the nanowires. The EDX line profile in Figure 3c displays a lower indium composition (around 15% lower) at the InGaAs bottom shell as compared to the InGaAs main layer formed above the height of GaAs (the EDX scanning area is indicated by the yellow arrow in the indium mapping of Figure 3a). We speculate this could be attributed to the different strain experienced by the InGaAs layer in radial and axial growth. The contrast in Figure 3b also indicates a lower indium composition along the six 〈112〉 direction lines from the GaAs core. This has been widely observed in other reported coaxial nanowires where a self-ordering effect reduces indium incorporation at the nanowire corners. [32] It also explains the dark lines observed in the side-view EDX mapping for indium in Figure 3a (marked in the In map in Figure 3a by a dashed line as a guide to the eye) which originate from the corners of the GaAs hexagon and rise up as the InGaAs growth takes place along both vertical and lateral directions. An atomically resolved image along the 〈110〉 zone axis is displayed in Figure 3d. The InGaAs exhibits a zincblende phase with high density twins as confirmed by the revealed "ABC" type stacking and the fast Fourier transform (FFT) image in Figure 3e. [33][34][35] Another thinned TEM lamella was also prepared using focused ion beam (FIB) to inspect the GaAs/Si interface in the mask opening, as shown by the high-resolution STEM image in Figure 3f. A 7 nm thick defect-free region was found above the GaAs/Si hetero-interface, followed by high density twinning through the wire.
To characterize the as-grown nanowire arrays on SOI substrate for PCSELs, we optically pumped a stretched honeycomb nanowire array with pulsed excitation using roomtemperature micro-photoluminescence (PL) spectroscopy. A supercontinuum source with a 633 nm laser wavelength and ≈100 ps pulse width at a 5 MHz repetition rate was used, illuminating the cavity from the top with a beam size of ≈6 µm in diameter. The cavity emission was collected from the top and analyzed using an InGaAs focal plane array detector connected to a spectrometer. We measured the PL emission at different pump powers. At a low excitation power, as shown in Figure 4a, a broad spontaneous emission appears between 1100 and 1300 nm and peaked at 1179 nm, corresponding to an indium solid phase composition of 0.27. [36] Increasing the pump power, a sharp lasing peak appears at 1252 nm and quickly dominates the spontaneous emission (Figure 4b). Accordingly, the peak full-width at half-maximum (FWHM) quickly drops to 1.1 nm around the threshold of 1.25 µJ cm −2 (Figure 4c). A slight blue-shift in the spontaneous emission peak, from 1179 to 1175 nm, is also observed at increased pump power, due to the band-filling effect. The lasing threshold fluence here is among the lowest reported values from bottom up nanowire PhC lasers. [15,[17][18][19][20] Further improved performance is expected with better overlapping of the gain material wavelength and the cavity resonance wavelength. We observe that the lasing wavelength closely matches the quadrupole bottom band-edge wavelength in our model. To confirm that the band-edge quadrupole mode is being excited, we calculated the band-edge frequency shift as the nanowire diameter increases and compared it against the observed lasing wavelengths from experimental samples. As shown in Figure 4d, with nanowire diameter increasing from 163 to 170 and 176 nm, the lasing wavelength follows the same trend as predicted by the band-edge modeling. This agrees well with the overall increase in volume-averaged refractive index. The ≈30 nm wavelength difference between the simulated band-edge and the lasing wavelength can be attributed to fabrication imperfections.
Since light confined in the PhC plane undergoes coherent oscillation and is coupled to the vertical direction through firstorder Bragg diffraction, [37] we expect the lasing emission from the PCSEL device to achieve narrow divergence. In Figure 5a, we consider the far field projection resulting from a PhC area of 35 µm 2 , equal to the optical pumping beam size experimentally used to achieve lasing. In our model, coherent oscillation from this area is enough to achieve sub-10° beam divergence. Figure 5b further plots the beam divergence as a function of the PhC cavity area by increasing the number of unit cells in the FDTD modeling. The beam divergence angle drops quickly with increasing PhC cavity area, approaching 3° divergence with PhC area over 60 µm 2 . In practice, however, in-plane coherence is expected to be limited by fabrication imperfections, and beam-widening effects such as thermal lensing also need to be considered. [38] Experimental measurement of the beam divergence, e.g., via back focal plane or Fourier plane imaging and spectroscopy, and fabricating electrically injected PCSELs for practical applications will be pursued in future work.
In addition to PCSEL devices, the ability to grow deformed honeycomb nanowire arrays in a single epitaxy provides a promising platform for building topological cavities. Figure 5c shows the SEM image of a hexagonal-shaped cavity by combining the compressed and stretched honeycomb nanowire lattices into a single device to generate topological interface modes. Although we are able to achieve PhC band edge mode lasing at 1300 nm coming from the compressed honeycomb lattice inside the hexagonal cavity, as shown in Figure 5d, topological edge mode lasing or topological bulk mode lasing [9] is yet to be realized. Further investigations will be needed to selectively excite the topological edge mode in a system where band-edge modes and PhC bulk modes are also present.

Conclusion
In conclusion, we have demonstrated a bottom-up InGaAs nanowire platform on SOI substrate for PhC surface-emitting lasers at telecom wavelengths. The nanowires are arranged into deformed honeycomb lattices using lithographically defined SAE to take advantage of the Γ point band-edge modes for high directional vertical emission. Through modeling and optical pumping of the cavity, we have demonstrated room-temperature, very low threshold lasing from both stretched and compressed honeycomb lattices, with far field simulations suggesting an angle divergence smaller than 10°. Our bottom-up approach can also be extended to other PhC cavity devices, including the topological bulk-and edge-mode lasers, that despite achieving remarkably superior performance to commercial VCSELs, have been challenging to fully integrate on Si to date.

Experimental Section
Nanowire Characterization: The sample was analyzed by STEM in a Thermo Fisher Spectra 300 TEM at an acceleration voltage of 300 kV. EDX was performed in STEM mode using a Thermo Fisher Super-X detector. The Thermo Fisher Velox software was used to analyze the EDX data.
Optical Characterization: The nanowire arrays were optically pumped at room temperature by a pulsed supercontinuum laser (model YSL SC-PRO 7) with 633 nm peak wavelength, ≈100 ps pulse width, and 5 MHz repetition rate. Normal incidence was employed in the micro-PL set up, in which the pumping source and the sample emission were focused and collected through a 50× Mitutoyo Plan Apo NIR Infinity Corrected Objective (NA = 0.65, 0.42 µm resolving power) and analyzed using a NIRvana 640 InGaAs focal plane array detector connected to a spectrometer (Acton SpectraPro SP-2750). The emission patterns from the nanowire arrays were captured by the 2D InGaAs detector.