A modified Shockley equation taking into account the multi-element nature of light emitting diodes based on nanowire...

In this work we study how the multi-element nature of light emitting diodes (LEDs) based on nanowire (NW) ensembles influences their current voltage (I-V) characteristics. We systematically address critical issues of the fabrication process that can result in significant fluctuations of the electrical properties among the individual NWs in such LEDs, paying particular attention to the planarization step. Electroluminescence (EL) maps acquired for two nominally identical NW-LEDs reveal that small processing variations can result in a large difference in the number of individual nano-devices emitting EL. The lower number of EL spots in one of the LEDs is caused by its inhomogeneous electrical properties. The I-V characteristics of this LED cannot be described well by the classical Shockley model. We are able to take into account the multi-element nature of such LEDs and fit the I-V characteristics in the forward bias regime by employing an ad hoc adjusted version of the Shockley equation. More specifically, we introduce a bias dependence of the ideality factor. The basic considerations of our model should remain valid also for other types of devices based on ensembles of interconnected p-n junctions with inhomogeneous electrical properties, regardless of the employed material system.