Mesoscopic Interference and Light Trapping in Semiconductor Nanowire Mats
Authors: Tom Strudley1, Claire Blejean1, Tilman Zehender2, Erik P.A.M. Bakkers2,3, Otto L. Muskens1,
1Faculty of Physical and Applied Sciences, University of Southampton, UK
2Dept of Applied Physics, Eindhoven University of Technology, Netherlands
3Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.
For many years the field of mesoscopic physics, defined as the interface between the microscopic and macroscopic worlds, has been the domain of solid state electronics. Amongst the most prominent of such mesoscopic effects are those of universal conductance fluctuations  and Anderson localization . The case of localization, in which transport is completely halted due to interference effects in the presence of sufficiently strong disorder, has been of considerable interest over the years. Indeed it was one of the two pieces of work for which Anderson was jointly awarded a Nobel prize in 1977, and its complexity has prompted many to quote Anderson’s Nobel lecture: “Very few believed it at the time…among those who failed to fully understand it at first was certainly its author.” 
Due to the strong analogy between electron and wave transport, such phenomena should also occur for wave transport in random media. However this presents a significant challenge, as mesoscopic effects occur when the probability of a diffusion scattering back to the same point and interfering with itself becomes significant. Intuitively this break down of the traditional ‘random walk’ description requires scattering mean free paths significantly lower than the wavelength. As a consequence, demonstrations of Anderson localization of light in three dimensions have proved difficult, with most observations being for other systems such as microwaves in a waveguide , acoustic waves  and even cold atoms . A couple of pioneering studies have reported localization of light in three dimensional media [7,8], however the interpretation of their results is complicated by absorption and fluorescence, which can mimic certain localization effects.
Figure 1: (left) The process of Vapour-liquid-solid growth starting from a gold nanoparticle catalyst is used to grow nanowires on a substrate. A lateral growth step increases the diameter of the wires, without affecting their length. (right) A typical high-density nanowire mat used in our experiments.
In our recent work published in Nature Photonics , we presented experimental results obtained using densely packed disordered mats of semiconductor nanowires. We demonstred strong mesoscopic effects using visible light in these layers. The nanowire mats were fabricated at the University of Eindhoven using the method of metallo-organic vapour phase epitaxy (MOVPE), see Fig. 1. By using a recipy of alternating cycles of vapour-liquid-solid (VLS) nanowire growth, followed by lateral growth to increase the wire diameter, precise control could be achieved over the length and diameters of the wire. A very high nanowire density of up to 50% area percentage was necessary to achieve the strong scattering strength required for observing the mesoscopic effects. These nanowire mats are remarkable as they have optical mean free paths as low as 0.2 micrometres, which along with their low intrinsic absorption make them ideal candidates for exploring Anderson localization.
Figure 2 [click on image to see higher resolution]: (left) typical intensity images of light transmitted through a nanowire mat, for a tight laser focus ('in focus') and for a laser illumination out of focus. Total image size ~20 μm. (middle) Intensity distribution normalized to ensemble average, showing the speckle fluctuations in space at the exit plane of the nanowire mat. (right) the total intensity fluctuations are enhanced for a tigthly focused laser, see Ref. .
By examining the intensity statistics of the transmitted light we found that it exhibited the large intensity fluctuations and long range correlations (both spatial and spectral) typical of mesoscopic interference (Fig. 2). Fitting these fluctuations with predictions from theory, we found an average of only 4 independent transmission channels through our sample, which is several orders of magnitude lower than previously reported values. These measurements unambiguously show for the first time that strong mesoscopic interference corrections can be achieved in three-dimensional nanomaterials and at optical wavelengths.
Mesoscopic transport corrections are a precursor of the strong or Anderson localization transition, where transport of light is halted by self-interference of many light paths returning to the same position in the medium. We are now in the exciting position where we can probe in detail the mesoscopic physics of light, as well as tuning our nanowire growth parameters further in a bid to observe localization itself. For practical applications, semiconductor nanowires have great potential in solar cell and light generation. A deep understanding of light transport in such materials is of great importance for further optimizing these applications. Ultimately, it may be possible for mesoscopic effects to be harnessed and turned into a new design tool for maximizing performance of real-world devices.
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