Copyright line will be provided by the publisher pss-Header will be provided by the publisher Review copy – not for distribution (pss-logo will be inserted here by the publisher) Designing InGaN/GaN nano-LED arrays for étendue-limited applications Sophia Fox *◊ , Simon O’Kane ◊ , Szymon Lis ◊ , Duncan Allsopp Department of Electronic and Electrical Engineering, University of Bath, Bath, BA2 7AY, UK Received ZZZ, revised ZZZ, accepted ZZZ Published online ZZZ (Dates will be provided by the publisher.) Keywords Please provide about four verbal keywords for your manuscript. * Corresponding author: e-mail saf24@bath.ac.uk ◊ Equal contributions from these authors This paper presents the far field results of a study by simulation using the finite-difference time-domain (FDTD) method of vertical light emitting diode structures with an incorporated ordered nanorod array in place of the typical surface roughened region. For a dipole placed directly below the centre nanorod in the FDTD model, highly collimated light is achieved by changing the radii of the nanorods, for a fixed array pitch, which we attrib- ute mainly to Bragg diffraction. By changing the pitch only, higher diffraction orders are observed in the far field emission as the pitch is increased and a relative in- crease in the directionality of emission is predicted. Copyright line will be provided by the publisher 1 Introduction InGaN/GaN nanorod LEDs are the subject of continuing interest owing to their enhanced light extraction efficiency [1, 2], and improved internal quantum efficiency (IQE) [2, 3]. In addition, the far field emission of nano-LEDs can be highly non-Lambertian [4] offering the prospect to use nanorod arrays in étendue limited ap- plications such as displays and image projectors [5, 6]. The directionality in the emission of nanorod arrays de- rives from two effects: diffraction [7-9] and optical wave- guiding along the axis of the nanorods [10]. Most work on nanorod LEDs has focused on structures in which the emissive quantum wells are located inside the nanorods themselves [1-3]. Whilst the reduced strain in such structures gives rise to an improved IQE, the reduc- tion in emissive volume compared with an equivalent pla- nar LED structure presents a challenge to achieving the same output power per unit area of the MQW. In principle light generated from a planar MQW lying below a nanorod array also may be coupled into, or interact with the latter to achieve a similar collimating effect on the emission. In such structures photonic crystal effects, including diffrac- tion, are expected [7, 11] as well as possible waveguiding in the nanorods. The requirement is to optimally couple light generated in the underlying slab-like structure into the nanorod array. This paper reports an investigation by finite-difference time-domain (FDTD) simulations of vertical LED struc- tures with an incorporated ordered nanorod array in place of the typical surface roughened region. Here it is shown that collimated emission can be realised using passive na- norod arrays. 2 Simulation setup The MIT developed software, MEEP [12], is used in the 3D FDTD simulations. The de- vice to be modelled in FDTD is shown in figure 1. The sil- ver reflector is assumed to be a perfect electrical conductor (PEC). The nanorod structure is a 7x7 hexagonal array comprised of nanorods with height of 850nm. The GaN slab below the nanorod array has a thickness of 1.85ȝm and the optical properties of GaN are modelled using a Drude-Lorentz model of a single oscillator [13]. The trans- verse dimensions of the GaN slab are assumed to be infi- nite. A perfectly matched layer with a width of 1ȝm is placed around the computational cell except for the base where we have the PEC boundary condition. The dipole is placed 250nm above the reflector either directly below the central nanorod in the 7x7 array or midway between the latter and a nearest neighbour. We run separate simulations for dipole polarisations E x and E y which are tangential to the reflector. The dipole is set to