Localization landscape theory of disorder in semiconductors I: Theory and modeling

摘要

We present here a model of carrier distribution and transport insemiconductor alloys accounting for quantum localization effects in disorderedmaterials. This model is based on the recent development of a mathematicaltheory of quantum localization which introduces for each type of carrier aspatial function called \emph{localization landscape}. These landscapes allowus to predict the localization regions of electron and hole quantum states,their corresponding energies, and the local densities of states. We show howthe various outputs of these landscapes can be directly implemented into adrift-diffusion model of carrier transport and into the calculation ofabsorption/emission transitions. This creates a new computational model whichaccounts for disorder localization effects while also capturing two majoreffects of quantum mechanics, namely the reduction of barrier height (tunnelingeffect), and the raising of energy ground states (quantum confinement effect),without having to solve the Schr\"odinger equation. Finally, this model isapplied to several one-dimensional structures such as single quantum wells,ordered and disordered superlattices, or multi-quantum wells, where comparisonswith exact Schr\"odinger calculations demonstrate the excellent accuracy of theapproximation provided by the landscape theory.