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

## TL;DR

This paper introduces a novel modeling approach using localization landscapes to predict quantum localization effects in disordered semiconductor alloys, enabling efficient carrier transport simulations without solving the Schrödinger equation.

## Contribution

It develops a new computational model integrating localization landscape theory into drift-diffusion simulations for disordered semiconductors, capturing quantum effects efficiently.

## Key findings

- Accurately predicts localization regions and energies of carriers.
- Replicates Schrödinger equation results in one-dimensional structures.
- Accounts for quantum tunneling and confinement effects without complex quantum calculations.

## Abstract

We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum localization which introduces for each type of carrier a spatial function called \emph{localization landscape}. These landscapes allow us to predict the localization regions of electron and hole quantum states, their corresponding energies, and the local densities of states. We show how 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 creates a new computational model which accounts for disorder localization effects while also capturing two major effects of quantum mechanics, namely the reduction of barrier height (tunneling effect), and the raising of energy ground states (quantum confinement effect), without having to solve the Schr\"odinger equation. Finally, this model is applied to several one-dimensional structures such as single quantum wells, ordered and disordered superlattices, or multi-quantum wells, where comparisons with exact Schr\"odinger calculations demonstrate the excellent accuracy of the approximation provided by the landscape theory.