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

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 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 Schrödinger 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 Schrödinger calculations demonstrate the excellent accuracy of the approximation provided by the landscape theory.

Localization landscape theory of disorder in semiconductors. II. Urbach tails of disordered quantum well layers

“…IV B of LL1 (Ref. 17) that the absorption spectrum calculated in a 1D disordered superlattices by the landscape theory agrees very well with the exact 1D Schrödinger calculation. Urbach tails computed from the 3D absorption model for an In 0.17 Ga 0.83 N/GaN structure at different applied biases are shown in Fig.…”

“…17) and its predictions account well for the experimental broadening of the below-gap absorption edge.…”

“…[14][15][16] Two companion papers, referred to as LL1 (Ref. 17) and LL3 (Ref. 16), describe the basis of the localization landscape (LL) theory and its application to transport and recombination in nitride heterostructure LEDs, respectively.…”

“…17), the LL theory is applied to the framework of semiconductors to derive a model accounting for quantum effects in disordered materials. In particular it is shown that the landscape u allows estimating in each localization subregion Ω m the fundamental localized eigenfunction and its corresponding eigenenergy as:…”

Optical absorption edge broadening in thick InGaN layers: Random alloy atomic disorder and growth mode induced fluctuations

“…[9][10][11] Recently, a series of theoretical works focusing on disorder in semiconductors based on a so-called localization landscape picture provided new insights into the optical features of optoelectronic devices relying on an InGaN/GaN quantum well (QW) medium. [12][13][14] Nonetheless, because many of the previous optical studies were performed on QWs grown along the polar c-axis, the subsequent analyses of this ternary alloy were plagued by the complexity of such systems. Indeed, the understanding of their optical properties is made more intricate compared to bulk layers due to additional difficulties in disambiguating the exact contribution due to QW thickness fluctuations from compositional fluctuations in emission and/or absorption features.…”