We present a model of carrier distribution and transport accounting for quantum localization effects in disordered semiconductor alloys. It is based on a recent mathematical theory of quantum localization which introduces a spatial function called localization landscape for carriers. These landscapes allow us to predict the localization of electron and hole quantum states, their energies, and the local densities of states. The various outputs of these landscapes can be directly implemented into a drift-diffusion model of carrier transport and into the calculation of absorption/emission transitions. This model captures the two major effects of quantum mechanics of disordered systems: the reduction of barrier height (tunneling) and lifting of energy ground states (quantum confinement), without having to solve the Schrödinger equation. Comparison with exact Schrödinger calculations in several one-dimensional structures demonstrates the excellent accuracy of the approximation provided by the landscape theory . This approach is then used to describe the absorption Urbach tail in InGaN alloy quantum wells of solar cells and LEDs. The broadening of the absorption edge for quantum wells emitting from violet to green (indium content ranging from 0% to 28%) corresponds to a typical Urbach energy of 20 meV and is closely reproduced by the 3D sub-bandgap absorption based on the localization landscape theory . This agreement demonstrates the applicability of the localization theory to compositional disorder effects in semiconductors.
 M. Filoche et al., Phys. Rev. B 95, 144204 (2017)
 M. Piccardo et al., Phys. Rev. B 95, 144205 (2017)
In this paper, we have analyzed and discussed the current spreading effect of the vertical LED depending
on different electrode patterns. A fully 2D model by solving drift-diffusion and Poisson equations is used to
investigate the current flow paths and radiative recombination region. The conventional vertical LED with and
without the transparent conducting layer has been considered to figure out the physical mechanism of the device.
With the examination of the separated electrode patterns, we find that the hole current spreading length is the
critical factor to influence the lighting region due to its relatively low mobility. The effect of the spacing and
geometry of the electrode pattern has been studied in this paper. We will present our work on modeling the
different geometric LED device and study the optimized condition for these chips.