Carrier transport in nanostructured materials, a NEGF perspective on localization landscape

The classic drift-diffusion model is not able to deal with superlattice or some other quantum structure, both at equilibrium and out of it. The Localization Landscape model is able to account those quantum effects by introducing a new effective potential calculated form a second order differential equation derived for the Schrödinger eigenvalue problem. This effective potential takes into account of the quantum effects by reshaping the original potential barriers seen by the electrons or holes, by lowering it when tunnelling effects are present or by increase the barrier height where quantum confinement occurs. This model allows also to predict the localization regions of carriers and their ground state energy and their local density of states. This new potential is introduced in already existing Poisson model in order to derive the carriers density and their confinement. Then, at equilibrium, this new developed model is compared with an exact Poisson-Schrödinger solver where the quantum effect are perfectly modelled by the wave nature of the electron and holes. Afterwards, the new effective potential is introduce in a classical Drift-Diffusion solver with the aim to derive the current density. The outputs of these simulations are put in parallel to the one founded with a non equilibrium Green function approach, where as a scattering model the Buttiker probes is introduced. These simulations are performed for several one-dimensional structures such as single quantum well and ordered and disordered superlattice with different periodicity, showing a promising match of the calculated output such as carriers density and current with respect to the already existing high computation demanding results.