Dimensional Dependence of Light Interaction with Nanowires
Authors:   , Wang Zhihuan , Nabet Bahram , Daryoush Afshin S. 
Published: July 2021

Semiconductor nanowires have been used in a variety of passive and active optoelectronic devices including waveguides, photodetectors, solar cells, LEDs, Lasers, sensors, and optical antennas. We examine GaAs/AlGaAs core-shell nanowires (CSNWs) grown on both GaAs and Si substrates by vapor-liquid-solid (VLS) method followed by Metal-Organic Chemical Vapor Deposition (MOCVD). These nanowires show extremely enhanced optical properties in terms of absorption, guiding, radiation of light, and even lasing. For the wavelength range of 700-1200nm these core-shells which only occupy 15% of the volume compared to thin films of the same height, reflect 2-4% of light for the CSNWs grown on Si, and 3-7% of light for those grown on GaAs substrate. The photoluminescence (PL) spectrum shows 923 times more light emitted from CSNWs grown on GaAs compared to bulk GaAs at room temperature, and optical pumped lasing with threshold of around 5 microwatt, followed by saturation near 12 microwatt. In addition, as-measured full-width half-max (FWHM) of ~13 ps time response has been demonstrated for CSNW using Electro-Optically Sampling (EOS) measurement. Analysis of the interaction of light with cylindrical and hexagonal structures with sub-wavelength diameters identifies both transverse and longitudinal plane modes which we generalize to volumetric resonant modes, importantly, without the need for vertical structures such as Bragg mirrors commonly used in vertical cavity surface emitting lasers (VCSEL's). We report on FDTD simulations with the aim of identifying the dependence of these modes on geometry (length, width), tapering, shape (cylindrical, hexagonal), core-shell versus core-only, and dielectric cores with semiconductor shells. This demonstrates how NWs form excellent optical cavities without the need for top and bottom mirrors. However, optically equivalent structures such as hexagonal and cylindrical wires can have very different optoelectronic properties meaning that light management alone does not sufficiently describe the observed enhancement in upward (absorption) and downward transitions (emission) of light in nanowires, rather, the electronic transition rates should be considered. Using Fermi's Golden Rule in interaction of light and matter, we discuss how the transition rates change due to electronic wave function and identify three factors, namely, oscillator strength, overlap functions, and the joint optical density of states(JDOS), explicitly contributing to the transition rates with strong dependence on dimensionality. We apply these results to the study of lasing in as-grown CSNW on Si & GaAs and discuss how these subwavelength structures can have enhanced optical gain, quantum efficiency and 175 times more optical output power compared to their bulk counterparts despite their large > 200nm geometries. These results and findings will further facilitate the design and optimization of sub-micron scale optoelectronic devices. In conclusion, we make a case for photonic integrated circuits that can take advantage of the confluence of the desirable optical and electronic properties of these nanostructures.