Diffusion models for atomic scale electron currents in semiconductor, p-n junction

TL;DR

This paper introduces a novel modeling approach for atomic-scale electron currents in semiconductors using Maximal Entropy Random Walk diffusion, capturing quantum-like localization effects for improved electronic device design.

Contribution

It presents a practical methodology for approximating electron flows at atomic scales, incorporating nonlinear effects and localization phenomena based on entropy-maximizing diffusion models.

Findings

Model reproduces quantum stationary probability densities.

Captures Anderson-like localization effects.

Provides a basis for designing future atomic-scale electronic components.

Abstract

While semiconductor electronics is at heart of modern world, and now uses 5nm or smaller processes of single atoms, it seems there are missing models of actual electron currents in these scales - which could help with more conscious design of future electronics. This article proposes such practical methodology allowing to model approximated electron flows in semiconductor, nonlinear Ohm law in p-n junction, and hopefully more complex systems e.g. built of transistors. It assumes electron hopping between atoms using Maximal Entropy Random Walk based diffusion - chosen accordingly to (Jaynes) maximal entropy principle, this way leading to the same stationary probability density as quantum models. Due to Anderson-like localization in nonhomogeneous lattice of semiconductor, electrons are imprisoned in entopic wells, e.g. requiring to exceed a potential barrier for conductance.